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New explicit and exact travelling wave solutions for a class of nonlinear evolution equations. (English) Zbl 0982.35101

Summary: With the help of Mathematica, many solutions for a class of nonlinear evolution equations \[ u_{tt}+ au_{xx}+ bu+ cu^2+ du^3= 0 \] are obtained by using the hyperbola function method and the Wu elimation methods, which include new travelling wave solutions, periodic solutions and kink soliton solutions. Some equations such as Duffing equation, sine-Gordon equation, \(\phi^4\) and Klein-Gordon equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35C05 Solutions to PDEs in closed form

Software:

Mathematica
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Full Text: DOI