Soliton resolution for the generalized complex short pulse equation with the weighted Sobolev initial data

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-11-28 DOI:10.1016/j.geomphys.2024.105387

Xianguo Geng , Feiying Yan , Jiao Wei

引用次数: 0

Abstract

In this work, the Cauchy problem for the generalized complex short pulse equation with initial conditions in the weighted Sobolev space

H (R)

is studied by using the Riemann-Hilbert method and the

\overline{\partial}

-steepest descent method. Based on the spectral analysis of the Lax pair, the solution of the Cauchy problem can be expressed as solution of a Riemann-Hilbert problem, which is transformed into a solvable model after a series of deformations. Finally, the long-time asymptotics and soliton resolution of the generalized complex short pulse equation in the soliton region are obtained by resorting to the

\overline{\partial}

-steepest descent method. The results also indicate that the N-soliton solutions of the generalized complex short pulse equation are asymptotically stable.

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具有加权Sobolev初始数据的广义复短脉冲方程的孤子解析

本文采用Riemann-Hilbert方法和∂挂号挂号-最陡下降法研究了加权Sobolev空间H(R)中具有初始条件的广义复短脉冲方程的Cauchy问题。基于Lax对的谱分析，Cauchy问题的解可以表示为Riemann-Hilbert问题的解，该问题经过一系列的变形后转化为可解模型。最后，利用∂∂-最陡下降法获得了广义复短脉冲方程在孤子区域的长时间渐近性和孤子分辨率。结果还表明，广义复短脉冲方程的n孤子解是渐近稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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