A Series of Soliton-like and Double-like Periodic Solutions of a (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation**The project supported by the National Outstanding Youth Foundation of China under Grant No. 19925522 and National Natural Science Foundation of China under Grant No. 90203001 and the Postdoctoral Science Foundation of China under Grant No. 2004035080

Abstract

We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik–Novikov–Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.