Exact solutions and optical soliton solutions for the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation

This paper studies the exact solutions with parameters and optical soliton solutions of the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation which describes space–time evolutions of slowly varying envelopes. When these parameters are taken special values, the optical solitary wave solutions are derived from the exact solutions. There are some integration tools that are adopted to retrieve soliton solutions. They are the modified simple equation method, the exp-function method, the soliton ansatz method and other two Sub-ODE methods. Bright–dark-singular soliton solutions and some trigonometric function solutions are obtained along with their respective constraint conditions. We compare between the results yielding from these integration tools. A comparison between our results in this paper and the well-known results is also given.