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 >= 0. 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

Yong LIANG. Solitary and periodic solutions of the generalized b-equation[J].Acta mathematica scientia,Series A, 0, (): 0-0.

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References

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Solitary and periodic solutions of the generalized b-equation

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