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.
Inverse scattering for the focusing nonlinear Schr\"odinger equation with elliptic background and full soliton gas
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abstract
In this manuscript we develop the direct and inverse scattering problem for the cubic focusing nonlinear Schr\"odinger equation and for initial data that are asymptotic to an elliptic travelling wave with distinct phase at $\pm \infty$. We consider the case in which the spectral bands intersect the real axis. We then show that this class of initial data has non zero intersection with the full soliton gas initial data.
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.