DYNAMICAL EVOLUTION STUDY FOR ONE-DIMENSIONAL SYSTEM WITH CUBIC-QUINTIC NONLINEARITY

Abstract

Nonlinear Schrodinger equation (NLSE) is a quantum system of nonlinear evolution， a kind of important equations, and in many areas have very important applications. Therefore, this type of equation models has important physical significance. People realized with GGPE describing BCS-BEC crossover, GGPE began to be utilized in people's research. When GPE and polytropic approximation are combined, the nonlinear term becomes generalized cubic-quintic nonlinearity. And the model becomes one-dimensional generalized cubic-quintic nonlinear Schrodinger equation (GCQ-NLSE). Many prior work deal with the special circumstances GCQ-NLSE the CQ-NLSE, and need to introduce additional integrability condition. In this work, we use the phase and amplitude coupling Transform combined with F-expansion method to solve the one-dimensional GCQ-NLSE. We obtained its soliton solutions without introducing any integrable condition. We apply the analytical solution obtained to our quantitative analysis of dynamic behavior of the model, whose results are dependent on the polytropic index which is related to the intensity of soliton strength, speed, system phonon velocity, these are depicted pictorially.