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Lump and Interaction Solutions to Linear (4+1)-Dimensional PDEs

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Abstract

Taking a class of linear (4+1)-dimensional partial differential equations as examples, we would like to show that there exist lump solutions and interaction solutions in (4+1)-dimensions. We will compute abundant lump solutions and interaction solutions to the considered linear (4+1)-dimensional partial differential equations via symbolic computations, and plot three specific solutions with Maple plot tools, which supplements the existing literature on lump, rogue wave and breather solutions and their interaction solutions in soliton theory.

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Authors and Affiliations

  1. College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090, China

    Wen-Xiu Ma

  2. Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

    Wen-Xiu Ma

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620, USA

    Wen-Xiu Ma

  4. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Wen-Xiu Ma

  5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Wen-Xiu Ma

  6. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

Authors
  1. Wen-Xiu Ma
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Correspondence to Wen-Xiu Ma.

Additional information

The work was supported in part by NSFC (11301331, 11371086, 11571079 and 51771083), NSF under the grant DMS-1664561, Shanghai Pujiang Program (14PJD007), the Natural Science Foundation of Shanghai (14ZR1403500), Natural Science Fund for Colleges and Universities of Jiangsu Province under the grant 17KJB110020, Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT under Grant No. 2017XKZD11, and the Distinguished Professorships by Shanghai University of Electric Power, China and North-West University, South Africa.

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Ma, WX. Lump and Interaction Solutions to Linear (4+1)-Dimensional PDEs. Acta Math Sci 39, 498–508 (2019). https://doi.org/10.1007/s10473-019-0214-6

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  • DOI: https://doi.org/10.1007/s10473-019-0214-6

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