Eur. Phys. J. Plus (2020) 135: 494
https://doi.org/10.1140/epjp/s13360-020-00463-z

Regular Article

Determining lump solutions for a combined soliton equation in (2+1)-dimensions

¹ School of Mathematical and Physical Sciences, Xuzhou University of Technology, 221111, Xuzhou, Jiangsu, People’s Republic of China
² Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, People’s Republic of China
³ Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
⁴ Department of Mathematics and Statistics, University of South Florida, 33620, Tampa, FL, USA
⁵ School of Mathematics, South China University of Technology, 510640, Guangzhou, People’s Republic of China
⁶ College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, Shandong, People’s Republic of China
⁷ Department of Mathematical Sciences, North-West University, Private Bag X2046, Mafikeng Campus, 2735, Mmabatho, South Africa

^b mawx@cas.usf.edu

Received: 1 October 2019
Accepted: 13 May 2020
Published online: 13 June 2020

Abstract

We consider a combined soliton equation involving three fourth-order nonlinear terms in (2+1)-dimensional dispersive waves and determine its lump solutions via symbolic computations. The combined equation is transformed into a Hirota bilinear equation under a logarithmic transformation and its lump solutions are computed explicitly in two cases of the coefficients in the model. Illustrative examples are presented, together with three-dimensional plots and contour plots of two specific lump solutions.