Method for finding optical solitons of generalized nonlinear Schrödinger equations

Abstract

Objective:New generalized Schrödinger equations with polynomial nonlinearities are considered. The Cauchy problem for these equations cannot be solved by the inverse scattering transform and optical solitons of these equations are looked for taking into account the traveling wave solutions. Method:Application of the well-known auxiliary equations as the Riccati equation and equations for elliptic functions for construction of solutions of new generalized Schrödinger equations is impossible right away. Therefore solutions of nonlinear ordinary differential equations are found using the transformations of dependent and independent variables. This extended approach allows us to obtain some new auxiliary nonlinear ordinary equations. Result:New auxiliary differential equations allow to look for optical solitons of the other generalized Schrödinger equations. We demonstrate that by using new auxiliary equations, we can find the optical solitons of the generalized nonlinear Schrödinger equations of the fourth degree with a polynomial of the eighteenth power.