The Hermitian symmetric space Fokas-Lenells equation: spectral analysis and long-time asymptotics

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

IMA Journal of Applied Mathematics Pub Date : 2022-09-07 DOI:10.1093/imamat/hxac025

Xianguo Geng, Kedong Wang, Mingming Chen

引用次数: 0

Abstract

Based on the inverse scattering transformation, we carry out spectral analysis of the $4\times 4$ matrix spectral problems related to the Hermitian symmetric space Fokas-Lenells equation, by which the solution of the Cauchy problem of the Hermitian symmetric space Fokas-Lenells equation is transformed into the solution of a Riemann-Hilbert problem. The nonlinear steepest descent method is extended to study the Riemann-Hilbert problem, from which the various Deift-Zhou contour deformations and the motivation behind them are given. Through some proper transformations between the corresponding Riemann-Hilbert problems and strict error estimates, we obtain explicitly the long-time asymptotics of the Cauchy problem of the Hermitian symmetric space Fokas-Lenells equation with the aid of the parabolic cylinder function. Keywords: Hermitian symmetric space Fokas-Lenells equation; Nonlinear steepest descent method; Spectral analysis; Long-time asymptotics.

查看原文本刊更多论文

厄密对称空间Fokas-Lenells方程:谱分析和长时间渐近性

基于逆散射变换，对厄米对称空间Fokas-Lenells方程的$4\ × 4$矩阵谱问题进行了谱分析，将厄米对称空间Fokas-Lenells方程的Cauchy问题的解转化为一个Riemann-Hilbert问题的解。将非线性最陡下降法推广到研究Riemann-Hilbert问题中，给出了各种Deift-Zhou轮廓变形及其背后的动机。通过相应的Riemann-Hilbert问题与严格误差估计之间的适当变换，我们借助抛物柱面函数明确地得到了hermite对称空间Fokas-Lenells方程的Cauchy问题的长期渐近性。关键词:厄密对称空间Fokas-Lenells方程;非线性最陡下降法;光谱分析;长期的渐近。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

IMA Journal of Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

8.30%

发文量

审稿时长

24 months

期刊介绍： The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered. The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.