LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES

doi:10.1007/s10473-019-0214-6

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 498-508.doi: 10.1007/s10473-019-0214-6

LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES

马文秀

College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China;Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

收稿日期:2018-01-24 出版日期:2019-04-25 发布日期:2019-05-06
作者简介:Wen-Xiu MA,mawx@cas.usf.edu
基金资助:
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.

LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES

Wen-Xiu MA

College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China;Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

Received:2018-01-24 Online:2019-04-25 Published:2019-05-06
Supported by:
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.

摘要/Abstract

摘要： 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.

关键词: symbolic computation, lump solution, interaction solution

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.

Key words: symbolic computation, lump solution, interaction solution

马文秀. LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES[J]. 数学物理学报(英文版), 2019, 39(2): 498-508.

Wen-Xiu MA. LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES[J]. Acta mathematica scientia,Series B, 2019, 39(2): 498-508.

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LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES

LUMP AND INTERACTION SOLUTIONS TO LINEAR(4+1)-DIMENSIONAL PDES

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