The classification of single traveling wave solutions for the fractional coupled nonlinear Schrodinger equation

The main purpose of this paper is to study the single traveling wave solutions of the fractional coupled nonlinear Schrodinger equation. By using the complete discriminant system method and computer algebra with symbolic computation, a series of new single traveling wave solutions are obtained, which include trigonometric function solutions, Jacobi elliptic function solutions, hyperbolic function solutions, solitary wave solutions and rational function solutions. As you can see, we give all the classification of single traveling wave solutions for the fractional coupled nonlinear Schrodinger equation. The obtained results substantially improve or complement the corresponding conditions in the literature (Esen and Sulaiman in Optik 167:150-156, 2018), (Eslami in Appl. Math. Comput. 258:141-148, 2016), (Han et al. in Phys. Lett. 395:127217, 2021). Finally, in order to further explain the propagation of the fractional coupled nonlinear Schrodinger equation in nonlinear optics, two-dimensional and three-dimensional graphs are drawn.