Soliton solution of stationary discrete nonlinear Schrödinger equation with the cubic-quintic nonlinearity

Abstract

This research discusses stationary discrete nonlinear Schrödinger equation with cubic-quintic nonlinearity. This equation is interesting to study because it has a unique solution known as a soliton. This solution has a fixed profile and speed when propagating and in the context of applications in the optical field, soliton can also be engineered as a carrier of information that can propagate on media with very long distances without experiencing significant interference. This paper only focuses on on-site type soliton (soliton that peak in the middle on one site). The method of determining solution on stationary discrete nonlinear Schrödinger equation with cubic-quintic nonlinearity is divided into two cases. The first case for the value of parameter C is zero and the soliton solution is determined analytically. In this case the soliton solution can be stated explicitly, therefore the soliton solution will be displayed and also the boundaries on the parameters that make the solution in the form of on-site soliton. The second case for the value of parameter C is not zero and the soliton solution is determined using a numerical approach namely Trust Region Dogleg Method. In this case the soliton solution cannot be stated explicitly, therefore only boundaries of the parameters that make the solution in the form of on-site soliton will be displayed.