Nonlinear waves described by the generalized Swift-Hohenberg equation

[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.

[发布机构] National Research Nuclear University, MEPhl (Moscow Engineering Physics Institute), Kashirskoe shosse 31, Moscow, Russia^1

[效力级别] 数学

[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