Solitons and other exact solutions for a class of nonlinear Schrödinger-type equations

Abstract

Recently, Zayed and Alurrfi have applied an extended auxiliary equation method for constructing the exact solutions of three nonlinear partial differential equations (PDEs) via the (2+1)-dimensional nonlinear cubic-quintic Ginzburg–Landau equation, the (1+1)-dimensional resonant nonlinear Schrödinger's equation with parabolic law nonlinearity and the (1+1)-dimensional nonlinear generalized Zakharov system of equations. In this article we apply a different method called a new mapping method proposed by Zeng and Yong for finding many other new exact solutions for the same three nonlinear PDEs mentioned above. Comparing the solutions resulting from these two different methods are given. The obtained results confirm that both the extended auxiliary equation method and the new mapping method are efficient techniques for analytic treatments of a wide variety of nonlinear PDEs in mathematical physics.