Rational solitary waves and optical solitons of the model having unrestricted dispersion and nonlinearity with polynomial form

Abstract

Objective:The mathematical model having unrestricted dispersion and nonlinearity in the polynomial form of described by the nonlinear Schrödinger equation is considered. Rational solitary wave solutions and optical solitons of the nonlinear partial differential equation are looked for. Method:The Painlevé test is applied to analyze the integrability of the nonlinear partial differential equation. Two variants of the simplest equation method are used for finding rational solitary waves and optical solitons of the mathematical model. Results:It is shown that the mathematical model having unrestricted dispersion and nonlinearity in the form of polynomial is nonintegrable by the inverse scattering transform. It is proved the general solution of the nonlinear ordinary differential equation has the expansion of in the Laurent series with two arbitrary constants. Rational solitary wave solutions and optical solutions of the mathematical model are found.