International Journal of Modern Physics B 2050162 (16 pages) © World Scientific Publishing Company DOI: 10.1142/S0217979220501623 Abundant fractional solitons to the coupled nonlinear Schr¨ odinger equations arising in shallow water waves N. Raza * and M. H. Rafiq † Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan * nauman.math@pu.edu.pk † hamzarafiq2525@gmail.com Received 17 February 2020 Revised 31 March 2020 Accepted 15 April 2020 Published 6 July 2020 In this work, the dynamics of wave phenomena modeled by (2 + 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. Keywords : Coupled nonlinear Schr¨odinger equations; local M-derivative; unified approach; dark and rational solitons. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fg 1. Introduction The analysis of exact solutions to nonlinear wave equations plays a significant role in the study of nonlinear physical phenomena. Finding exact solutions of these nonlinear wave equations, if possible, facilitates the validation of numerical solutions and helps to analyze the consistency of solutions. Over the last few decades, several new techniques have been developed to find exact solutions of nonlinear evolution equations (NLEEs). Some of these are the Hirota’s bilinear method, 1,2 the Bilinear transfor- mation method, 3 the Exp-function method, 4–6 the generalized Exp-function * Corresponding author. 2050162-1 Int. J. Mod. Phys. B Downloaded from www.worldscientific.com by CITY UNIVERSITY LONDON on 07/09/20. Re-use and distribution is strictly not permitted, except for Open Access articles.