Derives long-time asymptotics of a full arbitrary-genus dark soliton gas for defocusing NLS, yielding an N-dimensional Riemann-theta finite-gap solution with O(t^{-1}) or O(t^{-1/2}) errors in different sectors.
Arbitrary-genus dark soliton gases in the defocusing nonlinear Schr\"{o}dinger hydrodynamics
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The defocusing nonlinear Schr\"{o}dinger hydrodynamics supports exact dark solitons under finite density boundary conditions. However, the dark soliton gas, an interacting ensemble of dark solitons, has not yet been studied. In this work, we introduce an arbitrary-genus potential of dark soliton gases by considering the limit of the $\mathcal{N}$-dark soliton as $\mathcal{N}\to \infty$. The large-space asymptotics and long-time evolution of this dark soliton gas potential are analytically investigated through Deift-Zhou nonlinear steepest descent approach. The genus-$N$ dark soliton gas potential approaches the genus-$N$ finite-gap solution as $x \to -\infty$ and the background $1$ as $x \to +\infty$. In the long-time evolution, as the self-similar variable $\xi=x/t$ increases, the gas configuration exhibits a cascade of behaviours, passing from unmodulated and modulated genus-$N$ regions and progressively reducing the genus down to the planar region (unmodulated genus-$0$ region). Notably, the evolution of lower-genus soliton gases can be embedded within that of higher-genus gases, exhibiting identical dynamics within specific regimes. This phenomenon is encoded by the underlying spectra. We also include numerical validations, in perfect agreement with the theoretical predictions.
fields
nlin.SI 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
Long-time asymptotics for the full Camassa-Holm soliton gas are obtained from a limiting RH problem with two reflection coefficients, producing elliptic-function leading terms in three regions.
Derives explicit leading-order large-time asymptotics for a new KdV soliton gas with two nonzero reflection coefficients, expressed via Jacobi elliptic functions on a hyperelliptic surface.
citing papers explorer
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Long-time asymptotics of a full arbitrary-genus dark soliton gas for the defocusing nonlinear Schrodinger equation
Derives long-time asymptotics of a full arbitrary-genus dark soliton gas for defocusing NLS, yielding an N-dimensional Riemann-theta finite-gap solution with O(t^{-1}) or O(t^{-1/2}) errors in different sectors.
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Long-time Asymptotics of a Full Camassa-Holm Soliton Gas
Long-time asymptotics for the full Camassa-Holm soliton gas are obtained from a limiting RH problem with two reflection coefficients, producing elliptic-function leading terms in three regions.
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Large-time asymptotics of a new KdV soliton gas
Derives explicit leading-order large-time asymptotics for a new KdV soliton gas with two nonzero reflection coefficients, expressed via Jacobi elliptic functions on a hyperelliptic surface.