Ratliff2020_Article_PhaseDynamicsOfTheDystheEquati.pdf (2.62 MB)
Phase dynamics of the dysthe equation and the bifurcation of plane waves
journal contribution
posted on 2020-02-12, 14:23 authored by Daniel RatliffThe bifurcation of plane waves to localised structures is investigated in the Dysthe
equation, which incorporates the effects of mean flow and wave steepening. Through
the use of phase modulation techniques, it is demonstrated that such occurrences may
be described using a Korteweg–de Vries equation. The solitary wave solutions of this
system form a qualitative prototype for the bifurcating dynamics, and the role of mean
flow and steepening is then made clear through how they enter the amplitude and width
of these solitary waves. In addition, higher order phase dynamics are investigated,
leading to increased nonlinear regimes which in turn have a more profound impact on
how the plane waves transform under defects in the phase.
History
School
- Science
Department
- Mathematical Sciences
Published in
Water WavesVolume
2Pages
123–144Publisher
Springer Science and Business Media LLCVersion
- VoR (Version of Record)
Rights holder
© The Author(s) 2019Publisher statement
This is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/Acceptance date
2019-09-09Publication date
2019-10-08Copyright date
2020ISSN
2523-367XeISSN
2523-3688Publisher version
Language
- en
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Deposit date: 12 February 2020Usage metrics
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