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Breathers on elliptic function background for a generalized nonlinear Schrödinger equation with higher-order terms

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  • Lou, Yu
  • Zhang, Yi

Abstract

A generalized nonlinear Schrödinger equation with higher-order terms, which is derived as a model for the nonlinear spin excitations in the one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin, is investigated. Firstly, in view of Riccati equations associated with the Lax pair, the Darboux transformation of a generalized nonlinear Schrödinger equation is presented. Secondly, the complicated Jacobi elliptic functions as seed solutions are considered so that much more fascinating solutions and dynamical properties can be obtained. Based on the above discussion, breathers in the presence of two kinds of Jacobian elliptic functions dn and cn are constructed. Finally, the dynamical properties of such solutions are analyzed by drawing the three-dimensional figures. The structures of these solutions are influenced by the higher-order operator. More importantly, the method provided in this paper can also be adopted to construct breathers on the elliptic functions background of other higher-order nonlinear integrable equations.

Suggested Citation

  • Lou, Yu & Zhang, Yi, 2022. "Breathers on elliptic function background for a generalized nonlinear Schrödinger equation with higher-order terms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 22-31.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:22-31
    DOI: 10.1016/j.matcom.2022.02.001
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    References listed on IDEAS

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    1. Hai-Qiang Zhang & Bo Tian & Xiang-Hua Meng & Xing Lü & Wen-Jun Liu, 2009. "Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(2), pages 233-239, November.
    2. Lou, Yu & Zhang, Yi & Ye, Rusuo & Li, Miao, 2021. "Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
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