Extended trial equation method to generalized nonlinear partial differential equations. (English) Zbl 1284.35371

Gurefe, Yusuf; Misirli, Emine; Sonmezoglu, Abdullah; Ekici, Mehmet

Appl. Math. Comput. 219, No. 10, 5253-5260 (2013).

Summary: In this article, we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity. By use of this method, the exact traveling wave solutions including soliton solution, singular soliton solutions, rational function solution and elliptic integral function solution to one-dimensional general improved KdV (GIKdV) equation and \(R(m,n)\) equation are obtained. Also, a more general trial equation method is proposed.

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35C07	Traveling wave solutions
35C08	Soliton solutions
35C15	Integral representations of solutions to PDEs

Keywords:

extended trial equation method; GIKdV equation; \(R(m,n)\) equation; soliton solution; elliptic solutions