New exact solutions to the nonlinear Schrödinger equation with variable coefficients

Abstract

This paper is concerned with the nonlinear Schrödinger equations with variable coefficients. By analyzing the dynamical properties of equilibrium levels to the related Hamiltonian, some new dark solitons, bubble solutions and periodic solutions were obtained in the case that the value of the Hamiltonian is between two equilibrium levels. Furthermore, when the value of the Hamiltonian is 0 and the value of the Hamiltonian takes two equilibrium levels, the dynamical properties and exact solutions for the nonlinear Schrödinger equations with variable coefficients were investigated with the help of the complete discrimination system of polynomial.