(3 + 1)维Calogero-Bogoyavlenskii-Schiff方程的行波解
Traveling Wave Solutions of the (3 + 1)-Dimensional Calogero-Bogoyavlenskii-Schiff Equation
DOI: 10.12677/AAM.2021.108292, PDF,   
作者: 蔡妮平：成都信息工程大学应用数学学院，四川 成都
关键词: 行波；CBS方程；分岔；动力系统；Traveling Wave； CBS Equation； Bifurcation； Dynamical System
摘要: 在物理和数学中，研究非线性微分方程的解具有重要意义。方程的解在理解非线性现象的性质起着重要的作用。本文应用动力系统方法全面系统地研究了(3 + 1)维Calogero-Bogoyavlenskii-Schiff方程的各类行波解。通过将Calogero-Bogoyavlenskii-Schiff方程的行波系统转化为R3中的动力系统，得到了有界行波和无界行波存在的参数分岔的充分条件。通过复杂的椭圆积分，给出了(3 + 1)维Calogero-Bogoyavlenskii-Schiff方程的所有行波解的精确式。
Abstract: In this paper, we apply the dynamical system methods to investigate all types of traveling waves of (3 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff equation comprehensively and systematically. By transforming its traveling wave system into a dynamical system in R3, we obtain sufficient conditions of parameter bifurcation sets to ensure the existence of various traveling wave solutions. Besides, by calculating the complex elliptic integrals, we give the exact expressions of all traveling wave solutions of the (3 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff equation, including the bounded and unbounded ones.
文章引用：蔡妮平. (3 + 1)维Calogero-Bogoyavlenskii-Schiff方程的行波解[J]. 应用数学进展, 2021, 10(8): 2803-2815. https://doi.org/10.12677/AAM.2021.108292

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