Some novel solutions for the two-coupled nonlinear Schrödinger equations

We study an integrable two-coupled nonlinear Schrödinger (NLS) system by using the method of linear transformation. With the aid of the traveling wave solutions of the classical NLS equation, we can construct forty-eight different types of solutions for the two-coupled NLS system. Finally, we use numerical methods to compute the stability eigenvalue of the steady-state solution.