Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions

Abstract

In this study, we perform the extended Kudryashov method to nonlinear Schrödinger equation (NLSE) with spatio-temporal dispersion that arises in a propagation of light in nonlinear optical fibers, planar waveguides, Bose–Einstein condensate theory. Four types of nonlinearity – Kerr law, power law, parabolic law and dual-power law – are being considered for the model. By using this scheme, the topological, singular soliton and rational solutions are obtained. In addition, some graphical simulations of solutions are provided.It is demonstrated that the proposed algorithm is effective and can be handled for many other nonlinear complex differential equations.