Eur. Phys. J. Plus (2020) 135: 379
https://doi.org/10.1140/epjp/s13360-020-00366-z

Regular Article

Multi-lump or lump-type solutions to the generalized KP equations in -dimensions

¹ Normal School, Jinhua Polytechnic, Jinhua, 321007, Zhejiang, 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 Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

^* e-mail: jhchengli@126.com
^** e-mail: jhchengli66@163.com

Received: 11 September 2019
Accepted: 30 March 2020
Published online: 28 April 2020

Abstract

We aim to explore lump or lump-type solutions to the generalized Kadomtsev–Petviashvili (gKP) equations in -dimensions via the long wave limit technique. The construction procedure for presenting lump or lump-type solutions is improved. The key step is that all the involved parameters are extended to the complex field. We first furnish lump solutions from the corresponding soliton solutions to the -dimensional gKP equation. In particular, a general class of multi-lump solutions of the -dimensional gKP equation can be obtained. It is then shown that there exist lump-type solutions to the -dimensional gKPI equations with by means of the improved long wave limit technique.