New Exact Solutions for the Coupled Nonlinear Schr&amp;amp;#246;dinger Equations with Variable Coefficients

Yuting Qiu,Ping Gao

doi:10.4236/jamp.2020.88117

Abstract

In this paper, coupled nonlinear Schrodinger equations with variable coefficients are studied, which can be used to describe the interaction among the modes in nonlinear optics and Bose-Einstein condensation. Some novel bright-dark solitons and dark-dark solitons are obtained by modified Sine-Gordon equation method. Moreover, some figures are provided to illustrate how the soliton solutions propagation is determined by the different values of the variable group velocity dispersion terms, which can be used to model various phenomena.

Highlights

In nonlinear optics, the coupled nonlinear Schrödinger (CNLS) equations are often used to describe propagation of optical soliton in birefringence fibers, multimode fibers and optical fiber arrays
In this paper, coupled nonlinear Schrödinger equations with variable coefficients are studied, which can be used to describe the interaction among the modes in nonlinear optics and Bose-Einstein condensation
We study the evolution behavior of the dark-bright soliton solutions given by Equation (26), the bright-dark soliton solutions given by Equation (28), and interaction of the two solutions given by Equation (28), illustrated in the figures

Summary

Introduction

The coupled nonlinear Schrödinger (CNLS) equations are often used to describe propagation of optical soliton in birefringence fibers, multimode fibers and optical fiber arrays. Many researchers have studied the CNLS equation with constant coefficient. The evolutions of vector solitons for CNLS equation with constant coefficients are not dependent on any controllable parameters. We will consider the following coupled nonlinear Schrödinger equation with variable coefficients (VCNLS) [7]:. Exact traveling wave and soliton solutions of the VCNLS equation have been obtained by Zhong [10] using homogeneous balance principle and the F-expansion technique.

The Method

Exact Solutions for VCNLS

Case 1

Physical Application

Conclusion