Newell-Whiehead方程的精确解和解析近似解
Exact and Approximate Analytical Solutions of Newell-Whiehead Equation
摘要: 本文采用求解的平面动力系统方法研究Newell-Whiehead方程的精确解孤立波解和振荡解的解析近似解。文中对该方程有界行波解对应的平面动力系统做了详细的定性分析，并结合平面动力系统的理论知识作出了全局相图，依据全局相图，得到了该方程有界行波解的个数和大致性态方面的结论；并运用适当的方法求出了该方程在波速为时的两个精确扭状孤立波解，进一步求出了在波速较小时该方程振荡解的解析近似解。
Abstract: In this paper, the exact solitary wave solution and the analytical approximate solution of the Newell-Whiehead equation are studied by the plane dynamic system method for solving. In this paper, a detailed qualitative analysis of the plane dynamic system corresponding to the bounded traveling wave solution of the equation is made, and combined with the plane. The theoretical knowledge of the dynamic system has made a global phase diagram. According to the global phase diagram, the conclusions on the number of bounded traveling wave solutions and the approximate behavior of the equation are obtained. Using appropriate methods, the two exact twisted solitary wave solutions of the equation at wave speed are obtained, and the analytical approximate solution of the oscillatory solution of the equation when the wave speed is small, is further obtained.
文章引用：胡协奎. Newell-Whiehead方程的精确解和解析近似解[J]. 应用数学进展, 2021, 10(6): 2105-2112. https://doi.org/10.12677/AAM.2021.106220

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