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.
Large-space and large-time asymptotics for the mKdV soliton gas with any odd genus
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study the large-space and large-time asymptotic behavior of the soliton gas of genus $2n-1$ for the mKdV equation with $n\in \mathbb{N}_+$. As $x \to +\infty$, we show that the large-space asymptotics of the mKdV soliton gas can be expressed with the Riemann-theta function of genus $2n-1$. For large $t$, based on the nonlinear steepest descent method and $g$-function approach, we establish a global large-time asymptotic description of the mKdV soliton gas. The half-plane $\{(x,t):-\infty<x<+\infty, t>0\}$ is divided into $2n+1$ separated regions. In each region, the large-time asymptotics of the mKdV soliton gas is given by using the Riemann-theta functions and uniform error estimation.
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.