TRAVELING WAVE SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION VIA SINE-COSINE METHOD

Abstract

In this work, an analytical study of the two-dimensional nonlinear Schrodinger equation is presented, namely, the applicability of the sine-cosine method to search for the exact solution as a traveling wave. The widely known nonlinear Schrödinger equation plays an important role in the study of the theory of nonlinear waves in various fields of physics and has a huge number of exact solutions. This equation describes the evolution of the changing amplitude of nonlinear waves in various systems, such as weakly nonlinear and highly dispersive. One of the methods for obtaining exact solutions is the sine-cosine method. The advantage of this method is its simplicity and reliability in obtaining solutions to nonlinear problems. According to the method, the nonlinear evolution equation is reduced to the associated ordinary differential equations by wave transformation and then solved by sine or cosine functions. As a result of the applicability of the sine-cosine method, the traveling wave solutions are obtained for a two-dimensional nonlinear Schrodinger equation. 2D-graphs and 3D-graphs of the obtained solutions are shown.