On the existence of traveling wave solutions for cold plasmas

IF 2.7 3区 数学 Q1 MATHEMATICS, APPLIED
Diego Alonso-Orán , Angel Durán , Rafael Granero-Belinchón
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引用次数: 0

Abstract

The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field. First, using bifurcation theory, we can rigorously prove the existence of periodic traveling waves of small amplitude. Furthermore, our analysis also evidences the existence of different type of traveling waves. To this end, we present a second approach based on the analysis of the differential system satisfied by the traveling wave profiles, the existence of equilibria, and the identification of associated homoclinic and periodic orbits around them. The study makes use of linearization techniques, normal forms, and numerical computations to show the existence of different types of traveling wave solutions, with monotone and non-monotone behavior and different regularity, as well as periodic traveling waves.
关于冷等离子体行波解的存在性
本文讨论了作者在以前的工作中导出的用于近似磁场中无碰撞等离子体单向演化的渐近模型的行波解的存在性。首先,利用分岔理论,严格证明了小振幅周期行波的存在性。此外,我们的分析还证明了不同类型的行波的存在。为此,我们提出了第二种方法,该方法是基于对行波剖面所满足的微分系统的分析,平衡点的存在性,以及它们周围的相关同斜轨道和周期轨道的识别。本研究利用线性化技术、范式和数值计算证明了不同类型的行波解的存在性,这些行波解具有单调性和非单调性以及不同的正则性,并具有周期性行波。
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
Physica D: Nonlinear Phenomena
Physica D: Nonlinear Phenomena 物理-物理:数学物理
CiteScore
7.30
自引率
7.50%
发文量
213
审稿时长
65 days
期刊介绍: Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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