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Variational principle for singular waves

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  • He, Chun-Hui
  • Liu, Chao

Abstract

A variational formulation is extremely difficult to be established for a strongly nonlinear problem, and it is almost impossible for a singular differential equation without linear terms. This paper gives a universal approach to the establishment of a variational formulation of a singular travelling wave by the semi-inverse method. The basic properties of rogue waves are elucidated in an energy frame, and a Hamilton-like conversation law is proposed, which can be used for numerical treatment at the singular point.

Suggested Citation

  • He, Chun-Hui & Liu, Chao, 2023. "Variational principle for singular waves," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004678
    DOI: 10.1016/j.chaos.2023.113566
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    References listed on IDEAS

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    1. Chun-Hui He & Chao Liu, 2022. "A Modified Frequency–Amplitude Formulation For Fractal Vibration Systems," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-8, May.
    2. Ji-Huan He & Man-Li Jiao & Chun-Hui He, 2022. "Homotopy Perturbation Method For Fractal Duffing Oscillator With Arbitrary Conditions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-10, December.
    3. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
    4. Ji-Huan He & Wei-Fan Hou & Chun-Hui He & Tareq Saeed & Tasawar Hayat, 2021. "Variational Approach To Fractal Solitary Waves," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-5, November.
    5. Mohammed Elamine Sebih & Jens Wirth, 2022. "On a wave equation with singular dissipation," Mathematische Nachrichten, Wiley Blackwell, vol. 295(8), pages 1591-1616, August.
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    Cited by:

    1. Adel Elmandouh & Aqilah Aljuaidan & Mamdouh Elbrolosy, 2024. "The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation," Mathematics, MDPI, vol. 12(3), pages 1-15, January.

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