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.
