Bifurcation of traveling wave solutions for (1+1)-dimensional resonant nonlinear Schrödinger equation

Using the bifurcation theory method of dynamical systems, we study the phase portraits and exact traveling wave solutions of the (1+1) dimensional resonant nonlinear Schrödinger equation with parabolic law nonlinearity. Under different parameter conditions, we obtained various exact traveling wave solutions. In the limit case, the solitary wave solutions and the kink wave solutions can be obtained from the periodic wave solutions, and partial limiting process is given. Some previous results are extended.