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The exact solutions for the nonisospectral AKNS hierarchy through the inverse scattering transform

Author

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  • Ning, Tong-ke
  • Chen, Deng-yuan
  • Zhang, Da-jun

Abstract

Exact solutions for the nonisospectral AKNS hierarchy are obtained through the inverse scattering transform. Some explicit forms of these solutions are further given. Reductions are also considered. Exact solutions of some nonisospectral hierarchies, such as the nonisospectral mKdV hierarchy, the nonisospectral KdV hierarchy, the nonisospectral nonlinear Schrödinger hierarchy and the nonisospectral sine-Gordon hierarchy, are obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:339:y:2004:i:3:p:248-266
    DOI: 10.1016/j.physa.2004.03.021
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    Citations

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    Cited by:

    1. Ning, Tong-ke & Zhang, Weiguo & Jia, Gao, 2009. "The exact solutions for a nonisospectral nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1100-1105.
    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.
    3. Ahmad Yuosef Alodat & Zalailah Salleh & Hafiza Aishah Hashim & Farizah Sulong, 2021. "Corporate governance and firm performance: empirical evidence from Jordan," Journal of Financial Reporting and Accounting, Emerald Group Publishing Limited, vol. 20(5), pages 866-896, August.
    4. Jian Zhang & Juan Yue & Zhonglong Zhao & Yufeng Zhang, 2023. "Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    5. Sheng Zhang & Siyu Hong, 2017. "Lax Integrability and Soliton Solutions for a Nonisospectral Integrodifferential System," Complexity, Hindawi, vol. 2017, pages 1-10, November.
    6. 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.
    7. Li, Qi & Chen, Deng-yuan & Zhang, Jian-bing & Chen, Shou-ting, 2012. "Solving the non-isospectral Ablowitz–Ladik hierarchy via the inverse scattering transform and reductions," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1479-1485.

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