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New explicit travelling wave solutions for a class of nonlinear evolution equations. (Chinese. English summary) Zbl 1202.35310

Summary: With the help of Mathematica, three travelling-wave solutions for a class of nonlinear evolution equations \(u_{tt}+au_{xx}+bu+cu^3=0\) are obtained by the trigonometric function method and the Wu elimination method. These include new travelling-wave solutions, bell-soliton solutions and kink-soliton solutions. Some equations such as the Duffing equation, Klein-Gordon equation, Landau-Ginzburg-Higgs equation and \(\phi^4\) equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35C05 Solutions to PDEs in closed form

Keywords:

Mathematica

Software:

Mathematica
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