Method for finding optical solitons of generalized nonlinear Schrodinger equations

Objective: New generalized Schrodinger equations with polynomial nonlinearities are consid-ered. 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 equa-tions for elliptic functions for construction of solutions of new generalized Schrodinger 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 Schrodinger equations. We demonstrate that by using new auxiliary equations, we can find the optical solitons of the generalized nonlinear Schrodinger equations of the fourth degree with a polynomial of the eighteenth power.

Automated summary

This paper considers new generalized Schrodinger equations with polynomial nonlinearities. The inverse scattering transform cannot solve the Cauchy problem for these equations, hence, traveling wave solutions are sought for optical solitons. By using transformations of dependent and independent variables, solutions for nonlinear ordinary differential equations are found. These new auxiliary equations allow for the search for optical solitons of other generalized Schrodinger equations.