Orbital stability of solitary wave solutions of a Hamiltonian PDE arising in magma dynamics

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-09-28 DOI:10.1016/j.aml.2024.109326

Aiyong Chen, Xiaokai He

引用次数: 0

Abstract

We consider a Hamiltonian PDE arising from a class of equations appearing in the study of magma dynamics in the Earth’s interior. Previously, it has been shown that the Hamiltonian PDE admits solitary wave solutions. Simpson et al. proved that the solitary wave solutions are orbitally stable for the case

n = 2

. We verify the stability criterion analytically for the case

n = 3

. Our results answer partially an open question proposed by Simpson et al. (2008).

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岩浆动力学中出现的哈密顿 PDE 孤波解的轨道稳定性

我们考虑的是地球内部岩浆动力学研究中出现的一类方程中的哈密顿 PDE。此前已有研究表明，哈密顿 PDE 存在孤波解。Simpson 等人证明了孤波解在 n=2 的情况下是轨道稳定的。我们通过分析验证了 n=3 情况下的稳定性准则。我们的结果部分回答了辛普森等人（2008 年）提出的一个开放性问题。

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

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.