Optical solitons of the resonant nonlinear Schrodinger equation with arbitrary index

Traveling wave reduction of the resonant nonlinear Schr?dinger equation with arbitrary refractive index is considered. The system of equations for real and imaginary parts is presented. The first integrals for the system of equations are found. This system of equations is transformed to the only governing nonlinear ordinary differential equations of the first order. Exact solutions in the form of periodic and solitary waves of this nonlinear ordinary differential equation are given for various values of the refractive index.

Automated summary

The reduction of traveling waves of the resonant nonlinear Schrödinger equation with arbitrary refractive index is discussed in this study. The system of equations for the real and imaginary parts is presented and the first integrals for this system are found. The equations are transformed into a single governing nonlinear ordinary differential equation, and exact solutions in the form of periodic and solitary waves are provided for different values of the refractive index.