Click here to view fulltext PDF

Permanent link:
https://www.ias.ac.in/article/fulltext/pram/094/0043

Symbolic computation; lump solution; dispersion relation

This paper aims to explore a kind of lump solutions in nonlinear dispersive waves with higher-order rational dispersion relations.We show that the second member in the commuting Kadomtsev–Petviashvili hierarchy is such an example, and construct its lump solutions, based on a Hirota trilinear form. The presented lump solutions have one peak and two valleys, where the global maximum and minimum values are achieved. A few three dimensional plots and contour plots are made for a specific example of the lumps.

WEN-XIU MA^{1 2 3 4 5 6} LIQIN ZHANG^{3 7}

1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
2. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA
4. School of Mathematics, South China University of Technology, Guangzhou 510640, China
5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China
6. Department of Mathematical Sciences, North-West University,Mafikeng Campus,Mmabatho 2735, South Africa
7. College of Information Science and Artificial Intelligence, Xiamen Institute of Technology, Xiamen 361021, Fujian, China

Published

28 February 2020

Manuscript received

4 August 2019

Manuscript revised

21 November 2019

Accepted

12 December 2019

Early published

Unedited version published online

Final version published online

21 February 2020