Eur. Phys. J. Plus (2020) 135: 20
https://doi.org/10.1140/epjp/s13360-019-00049-4

Regular Article

Multi-wave, breather wave, and interaction solutions of the Hirota–Satsuma–Ito equation

¹ College of Computer, Jiangxi University of Traditional Chinese Medicine, Jiangxi, 330004, China
² Institute of Artificial Intelligence, Nanchang Institute of Science and Technology, Jiangxi, 330108, China

^* e-mail: 395625298@qq.com

Received: 7 June 2019
Accepted: 12 October 2019
Published online: 7 January 2020

Abstract

Under investigation is a (2+1)-dimensional generalized Hirota–Satsuma–Ito (gHSI) equation. Multi-wave solutions are presented using the three-wave method. Breather wave solutions are derived based on the homoclinic breather approach. Interaction solutions between lump and two solitary wave solutions are constructed via Hirota direct method. Through giving some special values to the parameters, dynamical behaviors of the obtained solutions are demonstrated in some 3D and contour plots.