Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger-type equations

Abstract

In this paper, we extended the auxiliary equation method proposed by Sirendaoreji and Kudryashov to construct new types of Jacobi elliptic function solutions of nonlinear partial differential equations (PDEs) in mathematical physics. The effectiveness of the extended method is demonstrated by applications to three nonlinear PDEs, namely, the (2+1)-dimensional nonlinear cubic–quintic Ginzburg–Landau equation, the (1+1)-dimensional resonant nonlinear Schrödinger’s equation with dual-power law nonlinearity and the generalized Zakharov system of equations. The solitary wave solutions or trigonometric functions solutions are obtained from the Jacobi elliptic function solutions when the modulus of the Jacobi elliptic functions approaches to one or zero, respectively. Comparison between our new results and the well-known results is given.