A study on lump solutions to a (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation

Yufeng Zhang; Wen-Xiu Ma; Jin-Yun Yang

doi:10.3934/dcdss.2020167

Article Contents

2020, Volume 13, Issue 10: 2941-2948. Doi: 10.3934/dcdss.2020167

This issue Previous Article Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation Next Article

A study on lump solutions to a (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation

1.
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
2.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
3.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
4.
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA
5.
School of Mathematics, South China University of Technology, Guangzhou 510640, China
6.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
7.
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa
8.
School of Mathematics and Physical Science, Xuzhou Institute of Technology, Xuzhou 221008, Jiangsu, China

^* Corresponding author: Wen-Xiu Ma
^* Corresponding author: Wen-Xiu Ma

Received: October 31, 2018

Revised: April 30, 2019

Early access: December 2019

Published: July 2020

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Abstract

We aim to generalize the (2+1)-dimensional Hirota-Satsuma-Ito (HSI) equation, passing the three-soliton test, to a new one which still has diverse solution structures. We add all second-order derivative terms to the HSI equation but demand the existence of lump solutions. Such lump solutions are formulated in terms of the coefficients, except two, in the resulting generalized HSI equation. As an illustrative example, a special completely generalized HSI equation is given, together with a lump solution, and three 3d-plots and contour plots of the lump solution are made to elucidate the characteristics of the presented lump solutions.

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Mathematics Subject Classification: Primary: 35Q51, 35Q53; Secondary: 37K40.

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Figure 1. Profiles of $ u $ when $ x = 0, 25, 50 $: 3d plots (top) and contour plots (bottom)

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