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

Hassan, M. M.

Commun. Theor. Phys. 53, No. 4, 596-604 (2010).

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.

MSC:

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

Keywords:

modified Zakharov-Kuznetsov equation; Schamel-Korteweg-de Vries equation; traveling and periodic wave solutions; extended mapping method