Chin. Phys. B, 2023, Vol. 32(2): 020201    DOI: 10.1088/1674-1056/ac7dc1
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# Matrix integrable fifth-order mKdV equations and their soliton solutions

Wen-Xiu Ma(马文秀)1,2,3,4,†
1 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
2 Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
3 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA;
4 School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa
Abstract  We consider matrix integrable fifth-order mKdV equations via a kind of group reductions of the Ablowitz-Kaup-Newell-Segur matrix spectral problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding Riemann-Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and construct their soliton solutions, when there are zero reflection coefficients. Illustrative examples of scalar and two-component integrable fifth-order mKdV equations are given.
Keywords:  matrix integrable equation      Riemann-Hilbert problem      soliton
Received:  23 May 2022      Revised:  10 June 2022      Accepted manuscript online:  02 July 2022
 PACS: 02.30.Ik (Integrable systems) 05.45.Yv (Solitons)
Fund: The work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11975145, 11972291, and 51771083), the Ministry of Science and Technology of China (Grant No. G2021016032L), and the Natural Science Foundation for Colleges and Universities in Jiangsu Province, China (Grant No. 17 KJB 110020).
Corresponding Authors:  Wen-Xiu Ma     E-mail:  mawx@cas.usf.edu

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