Bifurcations and solutions for the generalized nonlinear Schrödinger equation

Abstract

Abstract The theory of bifurcations for dynamical system is employed to construct new exact solutions of the generalized nonlinear Schrodinger equation. Firstly, the generalized nonlinear Schrodinger equation was converted into ordinary differential equation system by using traveling wave transform. Then, the system's Hamiltonian, orbits phases diagrams are found. Finally, six families of solutions are constructed by integrating along difference orbits, which consist of Jacobi elliptic function solutions, hyperbolic function solutions, trigonometric function solutions, solitary wave solutions, breaking wave solutions, and kink wave solutions.