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An Integrable Evolution System and Its Analytical Solutions with the Help of Mixed Spectral AKNS Matrix Problem

Author

Listed:
  • Sheng Zhang

    (School of Mathematical Sciences, Bohai University, Jinzhou 121013, China)

  • Jiao Gao

    (School of Mathematical Sciences, Bohai University, Jinzhou 121013, China)

  • Bo Xu

    (School of Mathematical Sciences, Bohai University, Jinzhou 121013, China
    School of Educational Sciences, Bohai University, Jinzhou 121013, China)

Abstract

In this work, a novel integrable evolution system in the sense of Lax’s scheme associated with a mixed spectral Ablowitz-Kaup-Newell-Segur (AKNS) matrix problem is first derived. Then, the time dependences of scattering data corresponding to the mixed spectral AKNS matrix problem are given in the inverse scattering analysis. Based on the given time dependences of scattering data, the reconstruction of potentials is carried out, and finally analytical solutions with four arbitrary functions of the derived integrable evolution system are formulated. This study shows that some other systems of integrable evolution equations under the resolvable framework of the inverse scattering method with mixed spectral parameters can be constructed by embedding different spectral parameters and time-varying coefficient functions to the known AKNS matrix spectral problem.

Suggested Citation

  • Sheng Zhang & Jiao Gao & Bo Xu, 2022. "An Integrable Evolution System and Its Analytical Solutions with the Help of Mixed Spectral AKNS Matrix Problem," Mathematics, MDPI, vol. 10(21), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3975-:d:953878
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    References listed on IDEAS

    as
    1. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
    2. Sheng Zhang & Siyu Hong, 2017. "Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System," Complexity, Hindawi, vol. 2017, pages 1-10, November.
    3. Ning, Tong-ke & Chen, Deng-yuan & Zhang, Da-jun, 2004. "The exact solutions for the nonisospectral AKNS hierarchy through the inverse scattering transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 248-266.
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