BIFURCATIONS AND EXACT SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATION WITH AN ANTI-CUBIC NONLINEARITY

Abstract

In this paper, we consider the nonlinear Schrödinger equation with an anti-cubic nonlinearity. By using the method of dynamical systems, we obtain bifurcations of the phase portraits of the corresponding planar dynamical system under different parameter conditions. Corresponding to different level curves defined by the Hamiltonian, we derive all exact explicit parametric representations of the bounded solutions (including periodic peakon solutions, periodic solutions, homoclinic solutions, heteroclinic solutions and compacton solutions).