Eur. Phys. J. Plus (2021) 136: 348
https://doi.org/10.1140/epjp/s13360-021-01321-2

Regular Article

Using the improved $exp(-\mathrm{\Phi }(\xi ))$ expansion method to find the soliton solutions of the nonlinear evolution equation

School of Science, Kaili University, 556011, Kaili, China

^a hnyangjuan1982@126.com

Received: 1 November 2020
Accepted: 13 March 2021
Published online: 31 March 2021

Abstract

With the help of the symbolic calculation software Mathematica, the nonlinear coupled Schrödinger system, (2 + 1)-dimensional dispersive long-wave system and (2 + 1)-dimensional Nizhnik–Novikov–Veselov system are solved by using the improved $exp(-\mathrm{\Phi }(\xi ))$ expansion method. Diverse new soliton solutions are obtained, and the structure and properties of soliton solutions are studied. We derive seven sets of exact solutions under different conditions for the nonlinear coupled Schrödinger system and the (2 + 1)-dimensional dispersive long wave equation, respectively, and for the (2 + 1)-dimensional Nizhnik–Novikov–Veselov system, we find the inelastic interaction solitary waves and fussion soliton.