Optical soliton solutions of the resonant nonlinear Schrödinger equation with Kerr-law nonlinearity

In this paper, we establish the exact solutions of the resonant nonlinear Schrödinger equation with Kerr law nonlinearity via the extended F-expansion method, improved tanh-coth expansion method and the first integral method. As the model is visualized under specific parameters, we establish the dynamical properties of the original equation, and give the Hamiltonian and topological properties of the equation. Subsequently, a new optical wave soliton solutions including singular soliton solution, periodic, peakon, dark and bright solitary wave solutions are obtained. As a result, it is verified that the methods used are effective to solve nonlinear partial differential equations in various fields of applied sciences.