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Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy

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  • Xiaohong Chen
  • Zine El Abiddine Fellah

Abstract

The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy. Then, based on the finite-order expansion of the Lax matrix, a hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to straighten out the associated flows, from which the algebro-geometric solutions of the (2+1)-dimensional integrable equation are proposed by means of the Riemann θ functions.

Suggested Citation

  • Xiaohong Chen & Zine El Abiddine Fellah, 2022. "Algebro-Geometric Solutions of a (2+1)-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-8, August.
    • Handle: RePEc:hin:jnlamp:4324648
    DOI: 10.1155/2022/4324648
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    Cited by:

    1. Xiaohong Chen & Tiecheng Xia & Liancheng Zhu, 2024. "A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions," Mathematics, MDPI, vol. 12(13), pages 1-11, June.

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