IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v172y2023ics0960077923004678.html
   My bibliography  Save this article

Variational principle for singular waves

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923004678
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113566?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Mohammed Elamine Sebih & Jens Wirth, 2022. "On a wave equation with singular dissipation," Mathematische Nachrichten, Wiley Blackwell, vol. 295(8), pages 1591-1616, August.
    3. 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.
    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. D. R. Solli & C. Ropers & P. Koonath & B. Jalali, 2007. "Optical rogue waves," Nature, Nature, vol. 450(7172), pages 1054-1057, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Liu-Qing & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Wang, Dong, 2022. "Bilinear form and nonlinear waves of a (1+1)-dimensional generalized Boussinesq equation for the gravity waves over water surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 494-508.
    2. Zhang, Yu & Li, Chuanzhong & He, Jingsong, 2016. "Rogue waves in a resonant erbium-doped fiber system with higher-order effects," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 826-841.
    3. Seadawy, Aly R. & Ali, Safdar & Rizvi, Syed T.R., 2022. "On modulation instability analysis and rogue waves in the presence of external potential: The (n + 1)-dimensional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Xi-zhong Liu & Zhi-Mei Lou & Xian-Min Qian & Lamine Thiam, 2019. "A Study on Lump and Interaction Solutions to a (3 + 1)-Dimensional Soliton Equation," Complexity, Hindawi, vol. 2019, pages 1-12, October.
    5. Li, Lingfei & Yan, Yongsheng & Xie, Yingying, 2022. "Rational solutions with non-zero offset parameters for an extended (3 + 1)-dimensional BKP-Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. Alexandra Völkel & Luca Nimmesgern & Adam Mielnik-Pyszczorski & Timo Wirth & Georg Herink, 2022. "Intracavity Raman scattering couples soliton molecules with terahertz phonons," Nature Communications, Nature, vol. 13(1), pages 1-6, December.
    7. He, Ji-Huan & Jiao, Man-Li & Gepreel, Khaled A. & Khan, Yasir, 2023. "Homotopy perturbation method for strongly nonlinear oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 243-258.
    8. Zhang, Yi & Sun, YanBo & Xiang, Wen, 2015. "The rogue waves of the KP equation with self-consistent sources," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 204-213.
    9. Wei, Peng-Fei & Long, Chun-Xiao & Zhu, Chen & Zhou, Yi-Ting & Yu, Hui-Zhen & Ren, Bo, 2022. "Soliton molecules, multi-breathers and hybrid solutions in (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani equation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    10. Yue-jun Deng & Rui-yu Jia & Ji Lin, 2019. "Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel’nikov System," Complexity, Hindawi, vol. 2019, pages 1-9, November.
    11. Jiang, Yan & Qu, Qi-Xing, 2021. "Solitons and breathers for a generalized nonlinear Schrödinger equation via the binary Bell polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 57-68.
    12. Bo Ren & Ji Lin & Zhi-Mei Lou, 2019. "A New Nonlinear Equation with Lump-Soliton, Lump-Periodic, and Lump-Periodic-Soliton Solutions," Complexity, Hindawi, vol. 2019, pages 1-10, June.
    13. El-Tantawy, S.A. & Salas, Alvaro H. & Alyousef, Haifa A. & Alharthi, M.R., 2022. "Novel approximations to a nonplanar nonlinear Schrödinger equation and modeling nonplanar rogue waves/breathers in a complex plasma," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    14. Wang, Haotian & Li, Xin & Zhou, Qin & Liu, Wenjun, 2023. "Dynamics and spectral analysis of optical rogue waves for a coupled nonlinear Schrödinger equation applicable to pulse propagation in isotropic media," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    15. Cao, Qi-Hao & Geng, Kai-Li & Zhu, Bo-Wei & Wang, Yue-Yue & Li, Ji-tao & Dai, Chao-Qing, 2023. "Annular rogue waves in whispering gallery mode optical resonators," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    16. Chen, Yi-Xiang, 2023. "Vector peregrine composites on the periodic background in spin–orbit coupled Spin-1 Bose–Einstein condensates," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    17. 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.
    18. Alim, Md. Abdul & Kawser, M. Abul, 2023. "Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    19. Miguel Onorato & Pierre Suret, 2016. "Twenty years of progresses in oceanic rogue waves: the role played by weakly nonlinear models," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 84(2), pages 541-548, November.
    20. Xianguo Geng & Ruomeng Li, 2019. "On a Vector Modified Yajima–Oikawa Long-Wave–Short-Wave Equation," Mathematics, MDPI, vol. 7(10), pages 1-23, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004678. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.