Optical envelope patterns in quadratic–cubic nonlinear medium by trial equation method

Abstract

In nonlinear optics, different forms of soliton propagation can be described by nonlinear Schrödinger equation. The purpose of this paper is to find and classify all exact solutions of a class of Schrödinger equation in quadratic-cubic nonlinear medium according to the quartic polynomial discriminant system and trial equation method. These solutions contain the partial solutions obtained by predecessors with different algorithms. The complete discriminant system of quartic polynomials is modified, and the eight families of exact solutions show various properties of patterns of amplitudes including singularity, periodicity and double periodicity.