Nonlinear Sciences
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The modified Mathieu and doubly confluent Heun equations emerge from Painlevé III3 and III1, yielding the dual gauge period.
· “From Painlev\'e equations to {cal N}=2 susy gauge theories: prolegomena”
A 1.67 kHz polarized signal synchronizes a 16.67 MHz laser's internal Q-switching envelope.
· “Nonlinear synchronization through vector subharmonic entrainment”
Competing next-nearest-neighbour coupling makes the decisive eigenvalue exponentially small; Borel-Padé fixes its prefactor and sign.
A tunable Weierstrass-ABC flow shows Lagrangian trajectories stay stochastic in the vanishing-noise limit.
Beyond a Thouless time, kicked many-body spectra reproduce COE, CUE, and CSE form factors to second order.
New manifold version gives birth, death, and split dates and shows ozone-depleted air mixing poleward.
Inverse neural-net analysis exposes a temporary interaction; refitting the equation restores its conservation law.
A deterministic model derives quantum tunneling from soliton statistics, with background noise setting the effective Planck constant.
· “Solitons, chaos, and quantum phenomena: a deterministic approach to the Schr\"odinger equation”
Adding quartic phase interactions turns oscillator networks into high-capacity analog associative memories.
· “Higher-Order Kuramoto Oscillator Network for Dense Associative Memory”
Tail shape decides whether two cavity solitons repel or bind, with coefficients from single-soliton data.
Fixed cycle-with-jumps wiring cuts median correlation-dimension error from 0.57 to 0.34 across 91 chaotic systems.
Signal pulses ride a parametric background, carrying combs to far-off wavelengths with one shared repetition rate.
· “Hyperparametric solitons in nondegenerate optical parametric oscillators”
Matching whole trajectories instead of estimating derivatives lets hidden moment equations emerge from irregular samples.
· “Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach”
Quantum revivals survive weak disorder but die near w≈2, when entanglement hits full-Hilbert-space random values.
· “Disordering a permutation symmetric system: revivals, thermalization and chaos”
Analytic solutions built from Richards growth and Hermite polynomials fit three cell lines with robust parameters.
· “On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions”
Near almost every point in either basin, arbitrarily close initial conditions head to the other attractor.
Scalar diffusivity equals renormalized viscosity; Kolmogorov constants follow from the same Craya-Herring calculation.
On a fixed n-soliton wave, every K- and tau-symmetry reduces to a mix of center and wave-number shifts.
Separating variables on a quintic curve yields theta-function solutions and a new Lax pair.
· “Linearization, separability and Lax pairs representation of a₄⁽²⁾ Toda lattice”
A reduction chain from 3×3 Lax matrices recovers the Adler-Yamilov map and new integrable birational YB maps.
· “Reductions and degenerate limits of Yang-Baxter maps with 3times 3 Lax matrices”
Two spectral-parameter conditions keep Kuznetsov-Ma breathers nonsingular; a new staggered breather obeys them too.
Scalar and fermion modes near the BTZ horizon show Wigner-Dyson spacing, a linear ramp, and Krylov peaks.
· “Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity”
Predictions for Mach stems and circular precursor fronts are confirmed by direct numerical simulation.
· “Obliquely interacting solitary waves and wave wakes in free-surface flows”
Smooth approximations of the sign rule keep the edge, so real hardware can use it.
· “How to Incorporate Higher-order Interactions in Analog Ising Machines”
Simulations track jet interfaces to reveal sub-Gaussian heights, fat-tailed speeds, and power-law spectra
· “Fluctuating interfaces in barotropic beta-plane turbulence”
Biomolecular condensates could classify high-dimensional molecular signals and control cell responses in one physical step.
· “Could Living Cells Use Phase Transitions to Process Information?”
Simulated tensegrity robot switches among crawling, swaying, and still states by changing which face touches the ground.
· “Multifunctional physical reservoir computing in soft tensegrity robots”
These are coherent structures that appear exactly where the weakly nonlinear Kuramoto-Sivashinsky approximation cannot reach.
Closed-form soliton profiles for a tunable phase-transition model, extended to the whole φ^4n family
· “Solitons of the Symmetric φ⁴-φ² |φ|-φ² Triple Well Model”
With slow Hebb-Oja plasticity, a 1D spiking ring visits chimera and bump states transiently; fast plasticity skips them.
· “Synchronization transitions in spiking networks with adaptive coupling”
Comparator and switches implement elastic collisions, so circuit tests can stand in for the mechanical system.
In two atmospheric-inspired chaotic tests, a neural network locks the simulator onto measured behavior.
Isostable-coordinate reduced models reproduce nonlinear forced responses, including period-doubling, that linearization misses.
· “Identification and Computation of Slow Manifolds Using the Isostable Coordinate System”
A periodic Feshbach modulation across the critical point erases domain walls, making the phase transition switchable.
Inhibitory links make slow-fast neurons chaotic; excitatory links lock them into phase-synchronized bursts.
· “Time series analysis of coupled slow-fast neuron models: From Hurst exponent to Granger causality”
An unsupervised network reads raw Hamiltonian entries and finds the same Poisson-to-GUE transition as spectral ratios.
One particle with separate x and y thermostats shows entropy production outrunning the standard quadratic near-equilibrium law.
· “Chaos in Nonequilibrium Two-Temperature (T_x, T_y) Nos\'e-Hoover Cell Models”
A 512-bit polynomial fit forecasts Lorenz-63 up to 105 Lyapunov times, versus 13 for past methods.
· “Machine-Precision Prediction of Low-Dimensional Chaotic Systems from Noise-Free Data”
Fundamental and second-harmonic waves carry equal, opposite currents, offering chip-scale chiral transport.
· “Chiral solitons in quadratic quasi-phase-matched photonic crystals”
A three-neuron pyloric motif holds one-third duty cycles from 0.5 to 30 s by tuning two half-activation voltages
· “Cellular Mechanisms of Phase Maintenance in a Pyloric Motif of a Central Pattern Generator”
A rank-16 affine map from the reflection coefficient to the initial field reaches ~7.5e-5 relative L2 error on held-out DPSK patterns.
With triadic interactions, a uniform lag produces period-doubling, chaos, and multistability.
Shape and confinement follow from the vector field alone, skipping long numerical runs.
· “Formation and Localization of Four-wing Attractor in Phase space”
The agreement survives the purely nonlinear, zero-precompression limit where the KdV approximation fails.
· “First-order continuum models for nonlinear dispersive waves in the granular crystal lattice”
Nearly lossless fiber loop lets a noise-seeded pulse break into soliton-on-background breathers, matching theory.
FF vortex, SH quadrupole, and TH anti-vortex form stable solitons in a checkerboard crystal.
· “Vortex solitons in quasi-phase-matched photonic crystals with the third harmonic generation”
Cyclic flipping energies let three-state spiral waves emerge from a six-state lattice, with shifted transition exponents.
· “Dynamic modes of active Potts models with factorizable numbers of states”
Even where the infinite-size theory predicts none, size-driven fluctuations make the jump; inertia delays it.
· “Finite size effect in Kuramoto oscillators with inertia on simplicial complex”
For the higher-order Gerdjikov–Ivanov equation, one equality unlocks W-, M-, multi-peak, anti-dark and periodic waves
Real oscillator networks are finite; this theory predicts their collective fluctuations below the mean-field threshold.
70-unit breather run predicts maximal breathers and random seas; assimilation plus norm rescaling extends the horizon.
· “Model-free Forecasting of Rogue Waves using Reservoir Computing”
A Lyapunov analysis yields explicit thresholds on coupling and distance for two moving oscillator clusters to lock together.
A thermodynamic-style Legendre pair selects operating points, sets stability, and explains why optimal networks form trees.
Closed-form GBDT formulas cover rogue-wave-like, periodic, step-like, and N-modulation regimes of focusing NLS.
New theorems tie quadrature solvability of the KdV Schrödinger equation to a vanishing reflection coefficient.
· “Solvability of the Korteweg-de Vries equation under meromorphic initial conditions by quadrature”
A fractional-order Hegselmann-Krause model still guarantees convergence and consensus, but only asymptotically.
Table 1 says which are k-contact, giving new solvable control systems and Cartan-geometry links.
Exact results: the only nonchaotic collapse is unstable, so the approach to the singularity is chaotic.
· “Some exact results on the Belinski-Khalatnikov-Lifshitz scenario”
When the same three people keep meeting, information stays in a small circle; three-way contact deepens the effect.
· “The recurrence of groups inhibits the information spreading under higher-order interactions”
One complex equation generates unmodulated oscillons; a two-Q-ball bound state explains their amplitude modulations.
Spatial correlations push the same odds to ~60%, giving experimenters two new tuning knobs.
Combines permutation entropy with extropy to flag dips in chaos that the older measure misses.
Second symplectic forms for Henon-Heiles, Kepler, and open Toda make multisymplectic integrators possible.
· “Multisymplectic structure of nonintegrable Henon-Heiles system”
Cheap off-the-shelf parts find max-cut partitions by locking oscillator phases into 0 and π.
Mass-spacing statistics of baryons and mesons match random-matrix theory; quark models and lattice QCD mostly do not.
· “Spectral-statistics properties of the experimental and theoretical light baryon and meson spectra”
Library signals teach a mapper to build and cold-start forecasters for short, unlabeled snippets.
· “Tailored Forecasting from Short Time Series via Meta-learning”
Non-reciprocal couplings make every site oscillate at one shared frequency, confirmed in 9- and 15-site circuits.
Pre-tension stiffens twisted shells; pre-compression flips diagonal patterns into twisted diamonds, matching experiments.
· “Buckling and post-buckling of cylindrical shells under combined torsional and axial loads”
Chaotic hopping between two wells creates the bursts; speed surges give early warning.
· “Extreme mixed-mode oscillatory bursts in the Helmholtz-Duffing oscillator”
A small change in how people perceive consensus turns gradual opinion change into abrupt polarization with hysteresis.
· “Explosive opinion spreading with polarization and depolarization via asymmetric perception”
Inverting the reservoir update turns readout training into a function of states and known weights alone.
· “Unsupervised Learning in Echo State Networks for Input Reconstruction”
Symmetry-aware spectral analysis shows symmetric plasma forcing silences one screech tone by cutting its feedback path.
· “Spectral dynamics of natural and forced supersonic twin-rectangular jet flow”
A mobility-weighted curl condition forces structured transverse currents, so weak additivity dominates strong in d>1.
Bottom and top bands in a clonal colony form by separate acid and base mechanisms, letting experiment tune each independently.
A simple nonlinear recursion is fully classified by the parity of p and the seed's position.
A one-dimensional model with memory effects matches full 3D simulations of solitary wave attenuation.
· “Slowly decaying strain solitons in nonlinear viscoelastic waveguides”
A perspective argues semantic information—correlations that keep a system alive—sets life apart and guides detection.
· “The Physics of Life: Exploring Information as a Distinctive Feature of Living Systems”
A middle drive layer synchronizes the two outer layers and sets their oscillation amplitude.
A conformable-fractional discretization gives provable stability and bifurcation thresholds for the coexistence state.
· “Bifurcation Analysis of Predator-Prey System using Conformable Fractional Order Discretization”
A stable rotating core grows from random initial conditions, with spin capped by the central density.
· “Vortices and rotating solitons in ultralight dark matter”
