zbMATH — the first resource for mathematics

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

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