Novel exact traveling wave solutions of Newton-Schrödinger system using Nucci reduction and Sardar sub-equation methods

Abstract

Abstract The main theme of this piece of research is to tackle a coupled Newton-Schrödinger type model. Two analytical techniques namely, Nucci reduction method and Sardar sub-equation methods have been employed to scrutinize exact traveling wave solutions. Through the application of these approaches, various solitary and traveling wave solutions including bright, dark and singular periodic solitons, have been obtained. Further, we have not only discussed the physical depiction of specific solutions but have also visually presented them through two dimensional (2D), three dimensional (3D), and density plots utilizing relevant parameter values. The extracted solutions show that the proposed methods are effective, simple, and successful in pinpointing the exact solution of models in engineering, optics, and other nonlinear disciplines.