On solving the nonlinear Schrödinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms

Abstract The soliton ansatz method, the tanh-coth method, the modified simple equation method, the new extended auxiliary equation method, the new mapping method, the rational ( G ′/ G )-expansion method and the generalized Kudryashov method are applied in this paper. Solitons and other solutions for nonlinear Schrodinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms have been found. The used methods present a wider applicability for handling the nonlinear partial differential equations. A comparison of our new results with the well-known results is made.