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Soliton and breather solutions for the Hirota equation on the elliptic function background

Author

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  • Lin, Tong-Tong
  • Dong, Huan-He
  • Zhang, Yi-Nuo
  • Song, Qi-Fang

Abstract

In this paper, we primarily focus our attention on the soliton and breather solutions of a Hirota equation on the backgrounds of elliptic functions such as cn and dn solution backgrounds. Firstly, the solution for the Lax pair of the Hirota equation in the genus-1 case is derived with the algebraic geometry method and subsequently expressed in a unified form with the theta functions. Following that, we deduce the soliton and breather solutions of that equation with the Darboux transformations. Finally, the maximum value of the solutions is derived with the MATLAB’s built-in functions.

Suggested Citation

  • Lin, Tong-Tong & Dong, Huan-He & Zhang, Yi-Nuo & Song, Qi-Fang, 2025. "Soliton and breather solutions for the Hirota equation on the elliptic function background," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002395
    DOI: 10.1016/j.chaos.2025.116226
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    References listed on IDEAS

    as
    1. Yu, Yaxuan & Wang, Qi & Zhang, Hongqing, 2005. "The extended Jacobi elliptic function method to solve a generalized Hirota–Satsuma coupled KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1415-1421.
    2. Li Cheng & Wen-Xiu Ma, 2023. "Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations," Mathematics, MDPI, vol. 11(19), pages 1-8, September.
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