Acta Mathematica Scientia

, Volume 39, Issue 2, pp 509–523 | Cite as

Riemann-Hilbert Problems of a Six-Component mKdV System and its Soliton Solutions

  • Wen-Xiu MaEmail author


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 

2010 MR Subject Classification

35Q53 37K10 37K20 


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The author would also like to thank Batwa S, Gu X, Ju L, Lafortune S, Malisoff M, Manukure S, McAnally M, Tian J, Wang F D, Yong Y L, Zhang H Q, and Zhou Y for their valuable discussions.


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  2. 2.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  4. 4.College of Mathematics and Systems ScienceShandong University of Science and TechnologyQingdaoChina
  5. 5.College of Mathematics and PhysicsShanghai University of Electric PowerShanghaiChina
  6. 6.International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical SciencesNorth-West University, Mafikeng CampusMmabathoSouth Africa

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