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Symbolic computations and exact and explicit solutions of some nonlinear evolution equations in mathematical physics. (English) Zbl 1181.35247

Summary: With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher’s equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called \(G'/G\)-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35A24 Methods of ordinary differential equations applied to PDEs
35-04 Software, source code, etc. for problems pertaining to partial differential equations

Software:

Mathematica
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