Exact solutions for the conformable fractional coupled nonlinear Schrödinger equations with variable coefficients

Abstract

In this work, the general algebraic method is proposed for finding some solutions of a conformable fractional coupled nonlinear Schrödinger equation with variable coefficients arising in inhomogeneous fibers with two orthogonal polarization states. With the aid of symbolic computations, many types of new soliton pulse and periodic pulse solutions including complex doubly periodic solutions, solitary wave solutions, and trigonometric function solutions are obtained. Some 3D and 2D numerical simulations about these solutions are portraited, which show the novelty and visibility of the dynamical structure and propagation behavior of the corresponding model. Moreover, we found the W-shaped soliton pulse and the periodic wave pulse can be effectively controlled by changing the relative parameters of the frequency coefficients and orders, which will help us to have a better understanding about the internal structure of this model.