Pith. sign in

REVIEW 4 major objections 5 minor 41 references

Nonlinear skin modes and fixed points

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Nonlinearity lets open-boundary skin modes in a one-dimensional lattice exist at energies that the semi-infinite spectrum forbids, so the open-boundary spectrum is not a subset of the semi-infinite spectrum.

desk verdict The fixed-point stability argument is a genuine contribution, but the headline claim that the nonlinear OBC spectrum is not a subset of the SIBC spectrum rests on finite-size shooting roots and needs a thermodynamic-limit check. read the letter →

arxiv 2411.12424 v3 pith:G2NKBAXE submitted 2024-11-19 nlin.PS physics.opticsquant-ph

C. Yuce This is my paper · ORCID
classification nlin.PSphysics.opticsquant-ph
keywords nonlinearskineffectnon-Hermitianlatticeopenboundaryconditionsfixedpointsshootingmethodscale-freelocalizationdarksolitontight-bindingmodel
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper studies a one-dimensional tight-binding lattice with asymmetric couplings and several types of on-site nonlinearity, asking how the non-Hermitian skin effect changes when nonlinearity is present. It argues that nonlinearity leaves the semi-infinite boundary spectrum unchanged—still the disk bounded by the linear periodic-boundary loop—but substantially reshapes the open-boundary spectrum, whose modes can appear at real energies outside that disk. The key mechanism is that on a finite lattice a field can satisfy the open-boundary condition $\psi_{N+1}=0$ while its infinite continuation would approach a nonzero fixed point rather than decay to zero, so open-boundary skin modes are no longer constrained by the semi-infinite spectrum. If this is correct, nonlinear skin modes are power-dependent, form continuous energy bands, can be degenerate at a single energy, and show power-energy discontinuities, none of which occur in the linear case.

What carries the argument

The central object is a fixed point of the nonlinear recurrence in Eq. (1): a value $a_0 e^{i\theta}$ such that continuing the field past some critical site $N_c$ leaves it unchanged, $\psi_{N_c+1}=\psi_{N_c+2}=\dots=a_0 e^{i\theta}$. There are zero and nonzero fixed points; the zero fixed point is stable exactly when $E$ lies inside the linear periodic-boundary loop $E=e^{ik}+\gamma e^{-ik}$, independent of the nonlinear parameters, while nonzero fixed points have energy windows of stability set by the nonlinearity. The shooting method converts the boundary-value problem into iterating from a guessed amplitude $\psi_1$ and scanning $(E,\psi_1)$ for roots of $\psi_{N+1}=0$, and the paper uses the stability of these fixed points to read off which energies admit skin modes. The load-bearing mechanism is that $\psi_{N+1}=0$ no longer forces $\psi_\infty=0$ once nonlinearity is present: a trajectory can satisfy open boundary conditions and then settle onto a nonzero fixed point, which is exactly why open-boundary modes can live at energies outside the semi-infinite region.

What would settle it

Continue the shooting solution that satisfies $\psi_{N+1}=0$ at some $E>1+\gamma$ to $n=10N$ with no boundary imposed: if the field does not stay zero but grows to the nonzero fixed point $a_0$, the claimed open-boundary mode is an artifact of truncating at $N$. A second check is to solve the stationary equation on lattices of increasing $N$ and see whether energies outside $[-E_c,E_c]$ persist or recede; if they vanish as $N\to\infty$, the claimed non-containment of the open-boundary spectrum is false.

Watch

Extended reading notes

Core claim

The central discovery, stated on the paper's own terms, is that the open-boundary-condition spectrum of a nonlinear non-Hermitian lattice is not a subset of its semi-infinite-boundary-condition spectrum. For the linear system, open-boundary energies are confined to the real interval $[-2\sqrt{\gamma},2\sqrt{\gamma}]$ inside the semi-infinite spectrum, but in the nonlinear case skin modes can occur at real energies $E>1+\gamma$, outside the semi-infinite region. The reason is a failure of the implication $\psi_{N+1}=0 \Rightarrow \psi_\infty=0$: a shooting solution can pass through zero at the right boundary and then rise to a nonzero fixed point if continued further, so the finite-lattice mode satisfies open boundary conditions even though it would not be a semi-infinite mode. The paper also finds that the open-boundary spectrum is real, continuous in energy, and multiply degenerate, and that these nonlinear skin modes disappear when the couplings become Hermitian ($\gamma=1$).

Load-bearing premise

The construction treats a finite-lattice solution with $\psi_0=\psi_{N+1}=0$ as a genuine open-boundary skin mode even when continuing the recurrence beyond site $N+1$ would make the field rise to a nonzero fixed point rather than decay to zero; if 'spectrum' is required to mean modes whose tail is compatible with the semi-infinite boundary condition, those extra energies disappear.

Editorial extensions

If this is right

  • For a finite lattice with asymmetric couplings, nonlinear open-boundary skin modes exist at real energies $E>1+\gamma$, outside the semi-infinite spectrum, so the open-boundary spectrum is strictly larger than the semi-infinite spectrum in the nonlinear regime.
  • The nonlinear open-boundary spectrum is a continuum of real energies rather than isolated points, and two or more distinct skin modes with different powers can share the same energy, a degeneracy absent in the linear system.
  • The semi-infinite spectrum remains bounded by the linear periodic-boundary loop for both linear and nonlinear cases, meaning the nonlinearity affects the spectrum only through the boundaries.
  • A single coupling impurity can generate right-localized modes whose spatial extent grows with system size but whose profile is neither skin-like nor scale-free, and can also create discrete dark and anti-dark solitons under periodic boundary conditions.
  • At $\gamma=1$ (Hermitian couplings), the zero fixed point loses stability and these nonlinear skin modes disappear, so the phenomena require broken reciprocity in the hopping amplitudes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The power-energy discontinuity suggests that in an experiment sweeping pump power or energy, one would observe sudden jumps in the localization profile of open-boundary skin modes; such jumps could serve as a direct signature of the fixed-point mechanism.
  • If the open-boundary spectrum truly is not a subset of the semi-infinite spectrum, the standard non-Bloch band-theoretic characterization—which identifies open-boundary spectra with the generalized Brillouin zone—would need a nonlinear generalization, possibly phrased in terms of fixed-point basins rather than decay rates.
  • The paper constructs these outside-the-loop modes as stationary solutions but does not prove their dynamical stability; a time-dependent linearization around them would either confirm their physical stability or restrict them to a finite-time window.
  • The impurity-tunable dark solitons, whose width can be enlarged by placing neighboring impurities, could plausibly be tested in coupled optical waveguide arrays and might offer an optical switching or trapping mechanism.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies a one-dimensional tight-binding lattice with asymmetric couplings (JL=1, JR=γ<1) and several nonlinearities. Using a numerical shooting method and a fixed-point analysis of the recurrence, the author claims that (i) the semi-infinite (SIBC) spectral region is identical to the linear PBC loop irrespective of nonlinearity; (ii) the open-boundary (OBC) spectrum is not a subset of the SIBC spectrum, with OBC modes at real energies outside the linear interval ±(1+γ); (iii) nonlinear OBC skin modes exhibit a continuum of energies, degeneracies, and power-energy discontinuities; and (iv) a coupling impurity produces localized modes that are neither skin nor scale-free, as well as dark and anti-dark solitons. The central conceptual tool is the stability of zero and nonzero fixed points of the nonlinear recurrence.

Significance. If the non-subset result were rigorously established, it would be a notable qualitative difference between linear and nonlinear non-Hermitian systems and would provide a constructive fixed-point perspective for building nonlinear skin modes. The paper has clear strengths: the zero-fixed-point stability argument in Sec. II is analytic and shows that nonlinear parameters do not enter the linearized perturbation equation for a0=0; the Ablowitz-Ladik example yields a closed-form stability condition for the nonzero fixed point; and the impurity-induced dark/anti-dark soliton construction is simple and analytically grounded. However, the central spectral claims rest on a numerical shooting study whose thermodynamic-limit interpretation is not provided, and at least one key assertion (the real-valued OBC spectrum) is presented as a numerical suggestion rather than a demonstrated fact. The significance is therefore conditional on a more careful treatment of finite-N versus thermodynamic-limit modes.

major comments (4)
  1. [Section II, Fig. 2] The abstract's claim that the OBC spectrum is not a subset of the SIBC spectrum is not established by the presented evidence. In Sec. II the author defines the OBC spectrum as the set of energies of 'stable skin modes localized at the left edge.' The modes used to support the non-subset claim, shown in Fig. 2, satisfy ψ_{N+1}(E,ψ1)=0 for finite N while the infinite-lattice continuation of the same recurrence tends to a nonzero fixed point rather than decaying to zero. Such a continuation is not localized at the left edge in any thermodynamic sense, and the finite-N boundary condition alone does not make it a skin mode. The author notes that the roots are 'almost the same' for N=5, 10, and 100 but gives no localization-length analysis, no N→∞ limit, and no argument that the modes are not finite-size artifacts of the right boundary. Without a demonstration that these modes persist as exponentially localized states in the thermodynamic limit, the central 'non-subset' statement overstates what the shooting calculation shows.
  2. [Section II] The assertion that the nonlinear OBC spectrum is real-valued is supported only by the sentence 'Our numerical calculations reveal that Nc does not take finite values when E is complex, suggesting that the nonlinear OBC spectrum is real valued.' This is a conjecture based on an undocumented numerical scan, not a proof or even a quantified numerical result. No complex-energy grid, tolerance, or convergence criterion is reported. Since the reality of the OBC spectrum is used to compare the nonlinear OBC interval with the linear interval ±2√γ, this claim is load-bearing and needs either an analytic argument or a fully documented numerical study.
  3. [Section II, Figs. 1(c)-(d)] The numerical shooting method is not described to the standard needed for the central claims to be assessable. The text does not state the root-finding algorithm, the tolerance for 'satisfying' ψ_{N+1}=0, the number of iterations, the sampling of the E and ψ1 continua, or the numerical precision used for Figs. 1(c), 1(d), and 2(a). The OBC spectrum, the continuum of energies, the degeneracies, and the power-energy discontinuities all follow from these roots, so the absence of any accuracy or convergence analysis is a load-bearing gap. A reader cannot reproduce or verify the spectral claims from the information given.
  4. [Section III, Fig. 3(a)] The claim that impurity-induced modes form 'a family of localized modes that are neither skin nor scale free localized modes' is not quantitatively substantiated. The profile shown in Fig. 3(a) is essentially a step: the field is zero up to N_c, rises sharply to a nonzero fixed-point value, and stays at that value until the right edge. This profile's support grows with N, and its 'localization length' in the direction away from the right edge is infinite (the field does not decay). The distinction from scale-free modes (whose localization length scales as N) is asserted without extracting any length scale from the data. A precise definition of localization for these modes and a scaling analysis in N are needed before the claimed new class of localized modes is established.
minor comments (5)
  1. [Throughout] The notation is inconsistent, e.g., 'ψN +1' appears alongside 'ψ_{N+1}', and several boundary conditions are written with spaces (ψ0 = ψN +1 = 0). The manuscript would benefit from a consistent formatting pass.
  2. [Fig. 1(c)] The 'scaled ψ_{N+1}' is not defined; the reader cannot tell whether the plotted function is normalized, and by what factor.
  3. [Sec. II] The sentence 'a0 = 0 and a0 ≠ 0 ensure SIBC (or OBC when Nc is finite) and PBC, respectively [39]' is cryptic; the role of footnote [39] is unclear and it should either be integrated into the main text or removed.
  4. [Abstract] The statement that 'nonlinear interactions are shown to have no impact on the spectral region' should be qualified as 'for the fixed-point skin modes constructed here,' since only the linear stability of the zero fixed point is analyzed.
  5. [Sec. III, Fig. 3(b)] The parameters in the inset of Fig. 3(b) appear inconsistent with the caption: the main panel uses p = p' = 150, while the inset is described at p = 50 with different impurity strengths; the caption should be checked for consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fixed-point and shooting derivations are self-contained; self-citations appear only in background/supporting roles.

full rationale

The central claims are derived in-text rather than imported. Equation (2) for the fixed-point amplitude follows by substituting the constant-tail ansatz into Eq. (1); the SIBC spectral region follows from linearizing Eq. (1) around the zero fixed point, yielding phi_{j+1}+gamma phi_{j-1}=E phi_j with phi_infty=0, which is a linear-stability calculation and not a restatement of the conclusion. The OBC-not-a-subset result is supported by explicit numerical shooting solutions satisfying psi_{N+1}=0 at N=5, 10, and 100 (Figs. 1(c) and 2), i.e., by solving the finite boundary-value problem rather than by fitting a parameter to the claimed answer. The continuum of OBC energies arises from the root sets of psi_{N+1}(E, psi_1)=0; although psi_1 is a tunable shooting seed, in the linear limit the same tuning does not produce a continuum of distinct modes, so the continuum is a genuine property of the nonlinear system. The self-citations [23] and [38] are used as background or for the qualitative statement that SIBC skin modes approximate OBC modes; they are not load-bearing for the fixed-point construction or the subset claim. The paper's numerical suggestion that the OBC spectrum is real-valued ('Our numerical calculations reveal...') is an unsupported completeness claim, but that is a correctness gap, not a circular reduction.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities, but its conclusions rest on hand-picked model parameters and on the assumption that the shooting construction covers all relevant modes. No external data or fitted constants are used, so free parameters are model choices rather than fits, but the lack of a systematic scan limits how much can be concluded about 'various nonlinearities'.

free parameters (4)
  • gamma (asymmetry ratio) = 0.2 in main figures
    Sets the hopping asymmetry; chosen by hand. The spectral and bifurcation results are mainly computed at gamma=0.2.
  • g1 (Kerr coefficient) = 1 for main Kerr results
    Nonlinearity strength; chosen by hand. Period-doubling and skin-mode figures use g1=1.
  • alpha, beta, g2, g3 (nonlinear parameter set) = 0 or 1, or ratios such as g1=2g2=5g3=1
    The model allows five independent nonlinear parameters, but the paper explores only a few combinations. General conclusions are extrapolated from these hand-picked values.
  • W1 (impurity strength) = 1 for impurity modes; -0.8 or +1 for solitons
    Chosen to make psi_{N+1}=0 at the right edge or to create the desired dark/anti-dark solitons; no selection rule is derived.
assumptions (4)
  • domain assumption Eq. (1) is a valid model for the nonlinear non-Hermitian skin effect.
    The paper starts with this generalized discrete nonlinear Schrodinger equation without deriving it from a Hamiltonian or experiment (Section II).
  • domain assumption The shooting method with arbitrary psi_1 enumerates all relevant stationary modes.
    Every root of psi_{N+1}(E,psi_1)=0 is treated as an OBC mode; no completeness or uniqueness proof is provided (Section II).
  • domain assumption Linear tail stability of fixed points determines global existence of skin modes.
    The perturbation is linearized to phi_{j+1}+gamma phi_{j-1}=E phi_j and the condition phi_infinity=0 is used to define the stability region (Section II).
  • standard math Nonzero fixed-point solutions of Eq. (2) are the relevant backgrounds for extended modes.
    Follows by substituting a constant amplitude into the recurrence; used to construct period-1 modes.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Nonlinear skin modes and fixed points." pith.science (2026). https://pith.science/paper/G2NKBAXE

@misc{pith2026241112424,
  author       = {Pith},
  title        = {Pith review of: Nonlinear skin modes and fixed points},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G2NKBAXE}},
  note         = {Machine review of arXiv:2411.12424}
}
read the original abstract

We investigate a one-dimensional tight-binding lattice with asymmetrical couplings and various type of nonlinearities to study nonlinear non-Hermitian skin effect. Our focus is on the exploration of nonlinear skin modes through a fixed-point perspective. The nonlinear interactions are shown to have no impact on the spectral region in the semi-infinite system; however, they induce considerable changes when boundaries are present. The spectrum under open boundary conditions is found not to be a subset of the corresponding spectrum under the semi-infinite boundary conditions. We identify distinctive features of nonlinear skin modes, such as degeneracy, and power-energy discontinuity. Furthermore, we demonstrate that a family of localized modes that are neither skin nor scale-free localized modes is formed with the introduction of a coupling impurity. Additionally, we show that an impurity can induce discrete dark and anti-dark solitons.

Figures

Figures reproduced from arXiv: 2411.12424 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The bifurcation diagram reveals the critical value [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. (b) shows the density plots for three specific modes with the same energy but different ψ1. These modes are OBC modes for N = 3 (ψ4 = 0) but not SIBC modes, as ψn eventually reaches the same fixed point. III. IMPURITY INDUCED MODES In the linear non-Hermitian lattice, a coupling impu￾rity may induce an extensive number of scale-free local￾ized states whose localization lengths scale with the sys￾tem size. Here, we s… view at source ↗
Figure 3
Figure 3. FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 39 canonical work pages

  1. [1]

    Edge states and topo- logical invariants of non-hermitian systems

    Shunyu Yao and Zhong Wang, “Edge states and topo- logical invariants of non-hermitian systems”, Phys. Rev. Lett. 121, 086803 (2018)

    work page 2018

  2. [2]

    It yields two types of solutions: the zero fixed point with a0 = 0 and nonzero ones with a0 ̸= 0, which are real-valued solutions of this equa- tion

    Ec) a0 (2) where Ec = 1 + γ. It yields two types of solutions: the zero fixed point with a0 = 0 and nonzero ones with a0 ̸= 0, which are real-valued solutions of this equa- tion. Unlike the zero fixed point, the nonzero one is E- dependent and appears when E > Ec (since a2 0 > 0). For example, a2 0 = E − Ec Ec in the case of the Ablowitz-Ladik nonlinearit...

    work page 2002

  3. [3]

    Non-Hermitian Boundary Modes and Topology

    Dan S. Borgnia, Alex Jura Kruchkov, and Robert-Jan Slager,“Non-Hermitian Boundary Modes and Topology”, Phys. Rev. Lett. 124, 056802 (2020)

    work page 2020

  4. [4]

    Topological Band Theory for Non-Hermitian Hamiltonians

    Huitao Shen, Bo Zhen, and Liang Fu, “Topological Band Theory for Non-Hermitian Hamiltonians”, Phys. Rev. Lett. 120, 146402 (2018)

    work page 2018

  5. [5]

    Correspon- dence between Winding Numbers and Skin Modes in Non-Hermitian Systems

    Kai Zhang, Zhesen Yang, and Chen Fang, “Correspon- dence between Winding Numbers and Skin Modes in Non-Hermitian Systems”, Phys. Rev. Lett. 125, 126402 (2020)

    work page 2020

  6. [6]

    Topological Origin of Non-Hermitian Skin Effects

    Nobuyuki Okuma, Kohei Kawabata, Ken Shiozaki, and Masatoshi Sato, “Topological Origin of Non-Hermitian Skin Effects”, Phys. Rev. Lett. 124, 086801(2020)

    work page 2020

  7. [7]

    The funneling effect in a non- Hermitian Anderson Model

    Z. Turker and C. Yuce, “The funneling effect in a non- Hermitian Anderson Model”, Phys. Scr. 99, 075028 (2024)

    work page 2024

  8. [8]

    Topo- logical funneling of light

    S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, A. Szameit, “Topo- logical funneling of light”, Science 6488, 311 (2020). 6

    work page 2020

Show all 41 references
  1. [9]

    Impurity in- duced scale-free localization

    Linhu Li, Ching Hua Lee, Jiangbin Gong, “Impurity in- duced scale-free localization”, Communications Physics 4, 42 (2021)

    2021

  2. [10]

    Non-Hermitian edge burst without skin localization

    C. Yuce and H. Ramezani, “Non-Hermitian edge burst without skin localization”, Phys. Rev. B 107, L140302 (2023)

    2023

  3. [11]

    Scale- free localization and PT symmetry breaking from local non-Hermiticity

    Bo Li, He-Ran Wang, Fei Song, and Zhong Wang, “Scale- free localization and PT symmetry breaking from local non-Hermiticity”, Phys. Rev. B 108, L161409 (2023)

    2023

  4. [12]

    Critical non- Hermitian skin effect

    L. Li, C. H. Lee, S. Mu, and J. Gong, “Critical non- Hermitian skin effect”, Nat. Commun. 11, 5491 (2020)

    2020

  5. [13]

    Anomalous skin effects in disordered systems with a single non-Hermitian impurity

    Paolo Molignini, Oscar Arandes, Emil J. Bergholtz, “Anomalous skin effects in disordered systems with a single non-Hermitian impurity”, Phys. Rev. Research 5, 033058 (2023)

    2023

  6. [14]

    Accumulation of scale-free localized states in- duced by local non-Hermiticity

    Cui-Xian Guo, Xueliang Wang, Haiping Hu, and Shu Chen, “Accumulation of scale-free localized states in- duced by local non-Hermiticity”, Phys. Rev. B 107, 134121 (2023)

    2023

  7. [15]

    Critical hybridization of skin modes in coupled non-Hermitian chains

    S. M. Rafi-Ul-Islam, Zhuo Bin Siu, Haydar Sahin, Ching Hua Lee, and Mansoor B. A. Jalil, “Critical hybridization of skin modes in coupled non-Hermitian chains”, Phys. Rev. Research 4, 013243 (2022)

    2022

  8. [16]

    Scaling rule in critical non-Hermitian skin effect

    Kazuki Yokomizo, Shuichi Murakami, “Scaling rule in critical non-Hermitian skin effect”, Phys. Rev. B 104, 165117 (2021)

    2021

  9. [17]

    Universal competitive spectral scaling from the critical non-Hermitian skin effect

    Fang Qin, Ye Ma, Ruizhe Shen, and Ching Hua Lee, “Universal competitive spectral scaling from the critical non-Hermitian skin effect”, Phys. Rev. B 107, 155430 (2023)

    2023

  10. [18]

    Uni- versal scalefree non-Hermitian skin effect near the Bloch point

    Wei Li, Zhoujian Sun, Ze Yang, and Fuxiang Li, “Uni- versal scalefree non-Hermitian skin effect near the Bloch point”, Phys. Rev. B 109, 035119 (2024)

    2024

  11. [19]

    Observation of scale-free localized states induced by non-Hermitian defects

    Xinrong Xie, et. al., “Observation of scale-free localized states induced by non-Hermitian defects”, Phys. Rev. B 109, L140102 (2024)

    2024

  12. [20]

    Scale- free non-Hermitian skin effect in a boundary-dissipated spin chain

    He-Ran Wang, Bo Li, Fei Song and Zhong Wang, “Scale- free non-Hermitian skin effect in a boundary-dissipated spin chain”, SciPost Phys. 15, 191 (2023)

    2023

  13. [21]

    From scale-free to An- derson localization: a size-dependent transition

    B Yilmaz, C Yuce, C Bulutay, “From scale-free to An- derson localization: a size-dependent transition”, Phys. Rev. B 110, 214206 (2024)

    2024

  14. [22]

    Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach

    Yongxu Fu, Yi Zhang, “Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach”, Phys. Rev. B 108, 205423 (2023)

    2023

  15. [23]

    Nonlinear non-Hermitian skin effect

    C. Yuce, “Nonlinear non-Hermitian skin effect”, Phys. Lett. A 408, 127484 (2021)

    2021

  16. [24]

    Exact Solution of Non-Hermitian Systems with Generalized Boundary Conditions: Size- Dependent Boundary Effect and Fragility of the Skin Ef- fect

    Cui-Xian Guo, Chun-Hui Liu, Xiao-Ming Zhao, Yanxia Liu, and Shu Chen, “Exact Solution of Non-Hermitian Systems with Generalized Boundary Conditions: Size- Dependent Boundary Effect and Fragility of the Skin Ef- fect”, Phys. Rev. Lett. 127, 116801 (2021)

    2021

  17. [25]

    Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase

    Motohiko Ezawa, “Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase”, Phys. Rev. B 105, 125421 (2022)

    2022

  18. [26]

    Tombuloglu, C

    S. Tombuloglu, C. Yuce, “Nonlinear waves in an anti- Hermitian lattice with cubic nonlinearity Commun. Non- linear Sci. Numer. Simulat. 83, 105106 (2020)

    2020

  19. [27]

    Nonlinear perturbation of a high-order exceptional point: Skin discrete breathers and the hierarchical power- law scaling

    Hui Jiang, Enhong Cheng, Ziyu Zhou and Li-Jun Lang, “Nonlinear perturbation of a high-order exceptional point: Skin discrete breathers and the hierarchical power- law scaling”, Chin. Phys. B 32, 084203 (2023)

    2023

  20. [28]

    Anomalous Single-Mode Lasing In- duced by Nonlinearity and the Non-Hermitian Skin Ef- fect

    Bofeng Zhu, et. al., “Anomalous Single-Mode Lasing In- duced by Nonlinearity and the Non-Hermitian Skin Ef- fect”, Phys. Rev. Lett. 129, 013903 (2022)

    2022

  21. [29]

    Reference [30] intro- duced the concept of solitons with self-induced topolog- ical nonreciprocity

    have explored the emergence of insensitive edge soli- tons in non-Hermitian topological lattices, which exhibit robustness against perturbations. Reference [30] intro- duced the concept of solitons with self-induced topolog- ical nonreciprocity. An experimental demonstration o...

    2025 arXiv

  22. [30]

    Skin modes in a nonlinear Hatano-Nelson model

    Bertin Many Manda, Ricardo Carretero-Gonzalez, Panayotis G. Kevrekidis, and Vassos Achilleos, “Skin modes in a nonlinear Hatano-Nelson model ”, Phys. Rev. B 109, 094308 (2024)

    2024

  23. [31]

    Insensitive edge solitons in non-Hermitian topological lattices

    Bertin Many Manda, Vassos Achilleos, “Insensitive edge solitons in non-Hermitian topological lattices”, Phys. Rev. B 110, L180302 (2024)

    2024

  24. [32]

    Solitons with Self-induced Topological Nonre- ciprocity

    Pedro Fittipaldi de Castro, Wladimir Alejandro Benal- cazar, “Solitons with Self-induced Topological Nonre- ciprocity”, arXiv:2405.14919

    arXiv

  25. [33]

    Nonlinear Non-Hermitian Skin Ef- fect and Skin Solitons in Temporal Photonic Feedback Lattices

    Shulin Wang, et. al., “Nonlinear Non-Hermitian Skin Ef- fect and Skin Solitons in Temporal Photonic Feedback Lattices”, arXiv:2409.19693

    arXiv

  26. [34]

    Non-Hermitian excitations in nonlinear topological lat- tice

    Vlad Simonian, Daria A. Smirnova, Maxim A. Gorlach, “Non-Hermitian excitations in nonlinear topological lat- tice”, Appl. Phys. Lett. 125, 131701 (2024)

    2024

  27. [35]

    Skin solitons

    I. Komis, Z. H. Musslimani, and K. G. Makris, “Skin solitons”, Opt. Lett. 48, 6525 (2023)

    2023

  28. [36]

    A class of stable nonlin- ear non-Hermitian skin modes

    Hamed Ghaemi-Dizicheh, “A class of stable nonlin- ear non-Hermitian skin modes”, Phys. Scr. 99, 125411 (2024)

    2024

  29. [37]

    The discrete nonlinear Schrodinger equation: A survey of recent results

    P.G. Kevrekidis, K. O. Rasmussen, and A.R. Bishop, “The discrete nonlinear Schrodinger equation: A survey of recent results”, Int. J. Mod. Phys. B 15, 2833 (2001)

    2001

  30. [38]

    Nonlinear differential- difference equations

    M. J. Ablowitz and J. F. Ladik, “Nonlinear differential- difference equations”, Journal of Mathematical Physics 16, 598 (1975)

    1975

  31. [39]

    The Discrete Nonlinear Schr¨ odinger Equation: Mathematical Analysis, Numerical Computa- tions, and Physical Perspectives

    P. G. Kevrekidis, “The Discrete Nonlinear Schr¨ odinger Equation: Mathematical Analysis, Numerical Computa- tions, and Physical Perspectives”, Springer: Berlin, Hei- delberg, New York (2009)

    2009

  32. [40]

    Stabilization of zero-energy skin modes in finite non-Hermitian lattices

    C. Yuce, H. Ramezani, “Stabilization of zero-energy skin modes in finite non-Hermitian lattices”, Phys. Rev. A 106, 063501 (2022)

    2022

  33. [41]

    However, this approach doesn’t provide insights into the behavior of nonlinear skin modes, but rather addresses extended modes

    |ψn|, rather than ψn itself, can converge to a fixed value. However, this approach doesn’t provide insights into the behavior of nonlinear skin modes, but rather addresses extended modes

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.