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

Dimitrios Mitsotakis; Denys Dutykh; John Carter

doi:10.1016/j.wavemoti.2016.09.008

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

Dimitrios Mitsotakis
, Denys Dutykh
, John Carter

Mathematics

Victoria University of Wellington
Seattle University

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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.

Original language	British English
Pages (from-to)	166-182
Number of pages	17
Journal	Wave Motion
Volume	70
DOIs	https://doi.org/10.1016/j.wavemoti.2016.09.008
State	Published - 1 Apr 2017

Keywords

Cnoidal waves
Finite element method
Solitary waves
Stability

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10.1016/j.wavemoti.2016.09.008

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abstract = "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.",

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author = "Dimitrios Mitsotakis and Denys Dutykh and John Carter",

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AU - Dutykh, Denys

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N2 - 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.

AB - 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.

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KW - Finite element method

KW - Solitary waves

KW - Stability

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JO - Wave Motion

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ER -

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

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Keywords

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