RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS

doi:10.1007/s10473-019-0215-5

Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (2): 509-523.doi: 10.1007/s10473-019-0215-5

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RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS

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:2017-12-04 Revised:2018-07-27 Online:2019-04-25 Published:2019-05-06
Supported by:
The work was supported in part by NSFC (11371326, 11301331, and 11371086), NSF under the grant DMS-1664561, the 111 project of China (B16002), the China state administration of foreign experts affairs system under the affiliation of North China Electric Power University, Natural Science Fund for Colleges and Universities of Jiangsu Province under the grant 17KJB110020, and the Distinguished Professorships by Shanghai University of Electric Power, China and North-West University, South Africa.

Abstract

Abstract: Based on a 4×4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed, through a reduced Riemann-Hilbert problem where an identity jump matrix is taken.

Key words: integrable hierarchy, Riemann-Hilbert problem, soliton solution

Wen-Xiu MA. RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS[J].Acta mathematica scientia,Series B, 2019, 39(2): 509-523.

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RIEMANN-HILBERT PROBLEMS OF A SIX-COMPONENT MKDV SYSTEM AND ITS SOLITON SOLUTIONS

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