广义b方程的孤立波解及周期波解

Abstract

Abstract:

The research of generalized $b$-equation mainly focuses on the case of $b\ge0$. This paper uses the bifurcation method to investigate the bifurcation, nonlinear wave solutions and dynamical characteristics of generalized $b$-equation with $b=-3$. Under certain parameter conditions, one obtains the bifurcation phase diagram of the equation. Meanwhile, a new phenomenon is found different from the case of $b>0$, in which an infinite number of periodic trajectories in the traveling wave system cross the singular line $\varphi=c$. The existence of solitary and periodic solutions is given, and the 15 exact expressions for nonlinear wave solutions are obtained.

Key words: Generalized $b$-equations, Qualitative theory, Bifurcation method, Solitary solutions, Periodic solutions

CLC Number:

O175.2

Yang Jiaopeng, Liang Yong. Solitary and Periodic Solutions of the Generalized b-equation[J].Acta mathematica scientia,Series A, 2024, 44(3): 670-686.

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Solitary and Periodic Solutions of the Generalized b-equation

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