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Riemann–Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions

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Abstract

Associated with a \(4\times 4\) matrix spectral problem, a six-component AKNS soliton hierarchy is presented, together with the first three nonlinear soliton systems. From an equivalent spectral problem, a kind of Riemann–Hilbert problems is formulated for a six-component system of fourth-order AKNS equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled fourth-order AKNS equations are worked out from a reduced Riemann–Hilbert problem where an identity jump matrix is taken.

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Acknowledgements

The work was supported also in part by 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. The author would also like to thank S. Batwa, X. Gu, X.Z. Hao, S. Manukure, M. Mcanally, Y.L. Sun, F.D. Wang, H. Wang, X.L. Yong, H.Q. Zhang and Y. Zhou for their valuable discussions.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wen-Xiu Ma

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wen-Xiu Ma

  3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China

    Wen-Xiu Ma

  4. College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, 200090, China

    Wen-Xiu Ma

  5. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

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  1. Wen-Xiu Ma
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Correspondence to Wen-Xiu Ma.

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Communicated by Pierangelo Marcati.

The work was supported in part by NSFC under the Grants 11371326, 11301331 and 11371086; and NSF under the Grant DMS-1664561.

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Ma, WX. Riemann–Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions. Comp. Appl. Math. 37, 6359–6375 (2018). https://doi.org/10.1007/s40314-018-0703-6

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  • DOI: https://doi.org/10.1007/s40314-018-0703-6

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