New solutions for the (2 + 1)-dimensional nonlinear Schrӧdinger equation

Abstract

New exact solutions to the (1 + 1)-dimensional nonlinear Schrӧdinger equation are obtained by means of the exponential function test method. Further, the solutions of the (2 + 1)-dimensional nonlinear Schrӧdinger equation are also obtained by using appropriate transformation and being based on solutions obtained. Among them several arbitrary parameters are involved to generate a large number of wave structures, they are the double solitons, breather solitons, periodic waves and rational rogue waves, which dynamical behavior are shown by digital images.

Keywords

• The nonlinear Schrӧdinger equation
• Exact solution
• Periodic waves
• Rogue waves
• Dynamical behavior