Cnoidal waves and solitons to three-coupled nonlinear schrodinger's equation with spatially-dependent coefficients

This paper uses the extended auxiliary equation method to obtain the exact solutions of the nonlinear Schrodinger equations with variable-coefficient. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, and Jacobi elliptic functions solutions are obtained. The solitons are guaranteed to exist, provided the chromatic dispersion coefficients are Riemann integrable. Further, some of the obtained solutions are presented by 3D and 2D graphs to demonstrate the behavior of solutions. The results show that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding various exact solutions of nonlinear evolution equations with variable coefficients in mathematical physics.