Abundant fractional solitons to the coupled nonlinear Schrödinger equations arising in shallow water waves

Abstract

In this work, the dynamics of wave phenomena modeled by (2[Formula: see text]+[Formula: see text]1)-dimensional coupled nonlinear Schrodinger’s equations with fractional temporal evolution is studied. The solutions of the equations are two monochromatic waves with nonlinear modulations that have almost identical group velocities. The unified approach along with the properties of the local M-derivative are used to obtain dark and rational soliton solutions. The restrictions on parameters ensure that these soliton solutions are persevering. Lastly, the influence of the fractional parameter upon the obtained results are evaluated and depicted through graphs.