On the Cauchy problem of defocusing mKdV equation with finite density initial data: Long time asymptotics in soliton-less regions

被引：5

作者：

Xu, Taiyang ^{[1
]}

Zhang, Zechuan ^{[1
]}

Fan, Engui ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 372卷

基金：

美国国家科学基金会;

关键词：

Defocusing mKdV equation; Riemann-Hilbert problem; partial differential steepest descent method; Long time asymptotics; Soliton-less regions; NONLINEAR SCHRODINGER-EQUATION; NONZERO BOUNDARY-CONDITIONS; RIEMANN-HILBERT PROBLEMS; STEEPEST DESCENT METHOD; EVOLUTION-EQUATIONS; INVERSE SCATTERING;

D O I：

10.1016/j.jde.2023.06.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the long time asymptotics for the solutions to the Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data. The present paper is the subsequent work of our previous paper [arXiv :2108 .03650], which gives the soliton resolution for the defocusing mKdV equation in the central asymptotic sector {(x, t) : |& xi;| < 6} with & xi; := x/t. In the present paper, via the Riemann-Hilbert (RH) problem associated to the Cauchy problem, the long-time asymptotics in the solitonless regions {(x, t) : | & xi; | > 6, | & xi; | = O(1)} for the defocusing mKdV equation are further obtained. It is shown that the leading term of the asymptotics is in compatible with the "background solution" and the error terms are derived via rigorous analysis.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页码：55 / 122

页数：68

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