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On the nonlinear dynamics of the traveling-wave solutions of the Serre system

Mitsotakis, Dimitrios ; Dutykh, Denys ; Carter, John

Wave Motion, April 2017, Vol.70, pp.166-182 [Tạp chí có phản biện]

ISSN: 0165-2125 ; E-ISSN: 1878-433X ; DOI: 10.1016/j.wavemoti.2016.09.008

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  • Nhan đề:
    On the nonlinear dynamics of the traveling-wave solutions of the Serre system
  • Tác giả: Mitsotakis, Dimitrios ; Dutykh, Denys ; Carter, John
  • Chủ đề: Solitary Waves ; Cnoidal Waves ; Stability ; Finite Element Method ; Solitary Waves ; Cnoidal Waves ; Stability ; Finite Element Method ; Applied Sciences ; Physics
  • Là 1 phần của: Wave Motion, April 2017, Vol.70, pp.166-182
  • Mô tả: We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes a high-order finite-element method with smooth, periodic splines in space and explicit Runge–Kutta methods in time. Other forms of solutions such as cnoidal waves and dispersive shock waves are also considered. The differences between solutions of the Serre equations and the Euler equations are also studied. •Highly accurate numerical methods are used to study properties of the Serre system.•Solitary waves are shown to be stable under various perturbations.•Some cnoidal waves are shown to be periodically unstable.•A new recurrence phenomenon is observed.
  • Ngôn ngữ: English
  • Số nhận dạng: ISSN: 0165-2125 ; E-ISSN: 1878-433X ; DOI: 10.1016/j.wavemoti.2016.09.008

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