Matrix integrable fifth-order mKdV equations and their soliton solutions

doi:10.1088/1674-1056/ac7dc1

中国物理B ›› 2023, Vol. 32 ›› Issue (2): 20201-020201.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

收稿日期:2022-05-23 修回日期:2022-06-10 接受日期:2022-07-02 出版日期:2023-01-10 发布日期:2023-01-10
通讯作者: Wen-Xiu Ma E-mail:mawx@cas.usf.edu
基金资助:
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).

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

Received:2022-05-23 Revised:2022-06-10 Accepted:2022-07-02 Online:2023-01-10 Published:2023-01-10
Contact: Wen-Xiu Ma E-mail:mawx@cas.usf.edu
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: matrix integrable equation, Riemann-Hilbert problem, soliton

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.

Key words: matrix integrable equation, Riemann-Hilbert problem, soliton

中图分类号: (Integrable systems)

02.30.Ik

05.45.Yv (Solitons)

Wen-Xiu Ma(马文秀). Matrix integrable fifth-order mKdV equations and their soliton solutions[J]. 中国物理B, 2023, 32(2): 20201-020201.

Wen-Xiu Ma(马文秀). Matrix integrable fifth-order mKdV equations and their soliton solutions[J]. Chin. Phys. B, 2023, 32(2): 20201-020201.

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Matrix integrable fifth-order mKdV equations and their soliton solutions

Matrix integrable fifth-order mKdV equations and their soliton solutions

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