New Exact Solutions of Two Nonlinear Physical Models

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.