Multi-Peak and Bright-Dark Solitary Wave Solutions of Higher-Order Dispersive Nonlinear Schrödinger Equations and their Applications

In mathematical physics, the Schrödinger equations have very important applications in Quantum mechanics, transmission lines, and optical fibers. The higher-order nonlinear Schrödinger equations (NLSEs) having higher-order dispersion, nonlinearity and cubic-quintic terms illustrates the propagation in optical fibers of enormously short pulses. In this paper, we construct the wave solutions of the higher-order NLSE with cubic-quintic dispersion and generalized second-order spatiotemporal dispersive NLSE by using the modified exponential rational function method (MERFM). As results, narrative solitons solutions in different forms are obtained, such as bright-dark solitons, trigonometric function, hyperbolic function, rational function, exponential function, singular solutions etc. The constructed results are compared with existing solutions in the literature which confirm that some have not been found in previous studies and their structures play an important role to explain a lot of physical phenomenon. Moreover, the structures of the newly obtained solutions are described by given appropriate parameters, and some interesting and novel graphs are obtained, which are helpful to explain the complicated physical phenomena of these nonlinear models. As consequence show the predominant and effectiveness of MERFM, which is also suitable for solving similar mathematical and physical models in other fields.