LONG-TIME ASYMPTOTIC BEHAVIOR FOR AN EXTENDED MODIFIED KORTEWEG-DE VRIES EQUATION

被引：25

作者：

Liu, Nan ^{[1
]}

Guo, Boling ^{[1
]}

Wang, Dengshan ^{[2
]}

Wang, Yupeng ^{[3
]}

机构：

[1] Inst Appl Phys & Computat Math, Beijing, Peoples R China

[2] Beijing Informat Sci & Technol Univ, Sch Appl Sci, Beijing, Peoples R China

[3] Minzu Univ China, Coll Sci, Beijing, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2019年 / 17卷 / 07期

基金：

中国国家自然科学基金; 北京市自然科学基金; 中国博士后科学基金;

关键词：

extended modified Korteweg-de Vries equation; Riemann-Hilbert problem; nonlinear steepest descent method; long-time asymptotics; NONLINEAR SCHRODINGER-EQUATION; STEEPEST DESCENT METHOD; RIEMANN-HILBERT PROBLEMS; HIROTA EQUATION; WAVES;

D O I：

10.4310/CMS.2019.v17.n7.a6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate an integrable extended modified Korteweg-de Vries equation on the line with the initial value belonging to the Schwartz space. By performing the nonlinear steepest descent analysis of an associated matrix Riemann-Hilbert problem, we obtain the explicit leading-order asymptotics of the solution of this initial value problem as time t goes to infinity. For a special case alpha=0, we present the asymptotic formula of the solution to the extended modified Korteweg-de Vries equation in region P = {(x, t) is an element of R-2 vertical bar 0<x <= Mt(1/5), t >= 3} in terms of the solution of a fourth order Painleve II equation.

引用

页码：1877 / 1913

页数：37

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