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    • Lump solutions with higher-order rational dispersion relations

      WEN-XIU MA LIQIN ZHANG

      Research Article Volume 94 Published: 28 February 2020 Article ID 0043

    • Fulltext

       

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

    • Keywords

       

      Symbolic computation; lump solution; dispersion relation

    • Abstract

       

      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.

    • Author Affiliations

       

      WEN-XIU MA1 2 3 4 5 6 LIQIN ZHANG3 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

    • Dates

       
      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

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