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Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System

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  • Sheng Zhang
  • Siyu Hong

Abstract

Searching for integrable systems and constructing their exact solutions are of both theoretical and practical value. In this paper, Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem and its time evolution equation are first generalized by embedding a new spectral parameter. Based on the generalized AKNS spectral problem and its time evolution equation, Lax integrability of a nonisospectral integrodifferential system is then verified. Furthermore, exact solutions of the nonisospectral integrodifferential system are formulated through the inverse scattering transform (IST) method. Finally, in the case of reflectionless potentials, the obtained exact solutions are reduced to -soliton solutions. When and , the characteristics of soliton dynamics of one-soliton solutions and two-soliton solutions are analyzed with the help of figures.

Suggested Citation

  • Sheng Zhang & Siyu Hong, 2017. "Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System," Complexity, Hindawi, vol. 2017, pages 1-10, November.
    • Handle: RePEc:hin:complx:9457078
    DOI: 10.1155/2017/9457078
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    References listed on IDEAS

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    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. 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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    Cited by:

    1. 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.
    2. Sheng Zhang & Yuanyuan Wei & Bo Xu, 2019. "Fractional Soliton Dynamics and Spectral Transform of Time-Fractional Nonlinear Systems: A Concrete Example," Complexity, Hindawi, vol. 2019, pages 1-9, August.

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