Large-space and large-time asymptotics for the mKdV soliton gas with any odd genus

2026/05/19 by Dedi Yan, Xianguo Geng, Kedong Wang · 1 voice · 2 citations
Physics and Astronomy · #nlin.SI

paper · pdf

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∈ ℕ₊. As x → +∞, 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):-∞<x<+∞, 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.

Citations

• Genus two KdV soliton gases and their long-time asymptotics
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Cited by

• Long-time asymptotics of a full arbitrary-genus dark soliton gas for the defocusing nonlinear Schrodinger equation
• Large-time asymptotics of a new KdV soliton gas

Discussions

• Dedi Yan, Xianguo Geng, Kedong Wang: Large-space and large-time asymptotics for the mKdV soliton gas with any odd genus https://arxiv.org/abs/2605.19934 https://arxiv.org/pdf/2605.19934 https://arxiv. [bsky, 0 points, 0 comments]

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