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Solving the non-isospectral Ablowitz–Ladik hierarchy via the inverse scattering transform and reductions

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  • Li, Qi
  • Chen, Deng-yuan
  • Zhang, Jian-bing
  • Chen, Shou-ting

Abstract

The non-isospectral Ablowitz–Ladik hierarchy is integrated by the inverse scattering transform. In contrast with the isospectral Ablowitz–Ladik hierarchy, the eigenvalues of the non-isospectral Ablowitz–Ladik equations in the scattering data are time-dependent. The multi-soliton solution for the hierarchy is presented. The reductions to the non-isospectral discrete NLS hierarchy and the non-isospectral discrete mKdV hierarchy and their solutions are considered.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:12:p:1479-1485
    DOI: 10.1016/j.chaos.2012.08.010
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    References listed on IDEAS

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    1. Lin, Runliang & Zeng, Yunbo & Ma, Wen-Xiu, 2001. "Solving the KdV hierarchy with self-consistent sources by inverse scattering method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 287-298.
    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.
    3. Zhang, Yi & Deng, Shu-fang & Zhang, Da-jun & Chen, Deng-yuan, 2004. "The N-soliton solutions for the non-isospectral mKdV equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 228-236.
    4. Ning, Tong-ke & Zhang, Da-jun & Chen, Deng-yuan & Deng, Shu-fang, 2005. "Exact solutions and conservation laws for a nonisospectral sine-Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 611-620.
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    Cited by:

    1. Song-Lin Zhao, 2020. "Soliton Solutions for a Nonisospectral Semi-Discrete Ablowitz–Kaup–Newell–Segur Equation," Mathematics, MDPI, vol. 8(11), pages 1-12, October.

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