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A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions

Author

Listed:
  • Xiaohong Chen

    (College of Science, Liaoning University of Technology, Jinzhou 121000, China)

  • Tiecheng Xia

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Liancheng Zhu

    (School of Electrical Engineering, Liaoning University of Technology, Jinzhou 121000, China)

Abstract

A new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy provide solutions of the new breaking soliton equation. Then, the new breaking soliton equation is decomposed into the systems of solvable ordinary differential equations. Finally, a hyperelliptic Riemann surface and Abel–Jacobi coordinates are introduced to straighten the associated flow, from which the algebro-geometric solutions of the new (2 + 1)-dimensional integrable equation are constructed by means of the Riemann θ functions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2034-:d:1425967
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    References listed on IDEAS

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    1. 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.
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