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On weakly singular and fully nonlinear travelling shallow capillary–gravity waves in the critical regime

Mitsotakis, Dimitrios ; Dutykh, Denys ; Assylbekuly, Aydar ; Zhakebayev, Dauren

Physics Letters A, 25 May 2017, Vol.381(20), pp.1719-1726 [Tạp chí có phản biện]

ISSN: 0375-9601 ; E-ISSN: 1873-2429 ; DOI: 10.1016/j.physleta.2017.03.041

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  • Nhan đề:
    On weakly singular and fully nonlinear travelling shallow capillary–gravity waves in the critical regime
  • Tác giả: Mitsotakis, Dimitrios ; Dutykh, Denys ; Assylbekuly, Aydar ; Zhakebayev, Dauren
  • Chủ đề: Capillary–Gravity Waves ; Peakons ; Nonlinear Dispersive Waves ; Capillary–Gravity Waves ; Peakons ; Nonlinear Dispersive Waves ; Physics
  • Là 1 phần của: Physics Letters A, 25 May 2017, Vol.381(20), pp.1719-1726
  • Mô tả: In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. •A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived.•Shallow...
  • Ngôn ngữ: English
  • Số nhận dạng: ISSN: 0375-9601 ; E-ISSN: 1873-2429 ; DOI: 10.1016/j.physleta.2017.03.041

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