扰动的扩展Zakharov-Kuznetsov方程行波解存在性
Existence of Traveling Wave Solutions for the Perturbed Extended Zakharov-Kuznetsov Equation
摘要: 扩展Zakharov-Kuznetsov (eZK)方程是描述磁化双温离子尘埃等离子体中三维非线性尘埃离子声孤波的重要数学模型，已被广泛应用于等离子体物理相关研究领域。本文聚焦受扰eZK方程的行波解特性，采用几何奇异摄动理论、Melnikov方法及不变流形理论，对该受扰方程进行系统分析。研究结果表明，带有外部Kuramoto-Sivashinsky扰动的eZK方程存在稳定行波解，且该方程系统可呈现极限环动力学行为。
Abstract: The extended Zakharov-Kuznetsov (eZK) equation is widely used to describe nonlinear three-dimensional dust-ion-acoustic solitary waves in a magnetized two-ion-temperature dusty plasma. This paper investigates the traveling wave solutions of the perturbed eZK equation. To analyze this perturbed equation, the geometric singular perturbation theory, Melnikov methods, and invariant manifold theory are employed to prove that the eZK equation with external Kuramoto-Sivashinsky perturbation has stable traveling wave solutions and also exhibits limit cycles.
文章引用：尚义杰, 李叶舟. 扰动的扩展Zakharov-Kuznetsov方程行波解存在性[J]. 理论数学, 2026, 16(4): 53-64. https://doi.org/10.12677/pm.2026.164091

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