New exact solutions of two nonlinear physical models. (English) Zbl 1219.35234

Summary: Abundant new exact solutions of the Schamel-Korteweg-de Vries (S-KdV) equation and modified Zakharov-Kuznetsov equation arising in plasma and dust plasma are presented by using the extended mapping method and the availability of symbolic computation. These solutions include the Jacobi elliptic function solutions, hyperbolic function solutions, rational solutions, and periodic wave solutions. In the limiting cases, the solitary wave solutions are obtained and some known solutions are also recovered.


35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C07 Traveling wave solutions
35B10 Periodic solutions to PDEs
35C11 Polynomial solutions to PDEs
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