Nonlinear waves described by the generalized Swift-Hohenberg equation

5th International Conference on "Problems of Mathematical and Theoretical Physics and Mathematical Modelling"

物理学;数学

Ryabov, P.N.^1 ; Kudryashov, N.A.^1

National Research Nuclear University, MEPhl (Moscow Engineering Physics Institute), Kashirskoe shosse 31, Moscow, Russia^1

关键词: Kink solution;    Mixed boundary-value problem;    Nonlinear waves;    Pseudo-spectral algorithms;    Soli-tary wave solutions;    Swift-hohenberg equations;    Traveling wave reductions;    Wave process;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/788/1/012032/pdf
DOI  :  10.1088/1742-6596/788/1/012032

来源: IOP

【 摘 要 】

We study the wave processes described by the generalized Swift-Hohenberg equation. We show that the traveling wave reduction of this equation does not pass the Kovalevskaya test. Some solitary wave solutions and kink solutions of the generalized Swift-Hohenberg equation are found. We use the pseudo-spectral algorithm to perform the numerical simulation of the wave processes described by the mixed boundary value problem for the generalized Swift-Hohenberg equation. This algorithm was tested on the obtained solutions. Some features of the nonlinear waves evolution described by the generalized Swift-Hohenberg equation are studied.