Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary–gravity waves

Jones, Mark

doi:10.1016/j.apm.2015.09.017

Cited by 2 publications

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References 28 publications

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“…They are not valid when M=2N or 3N. For details of these cases see [4,7,25,27,29,38,40,41] .They are generalisations and simplifications of the equations to be found in [23] and should be compared with those in [26] where the perturbations take a slightly different form. A similar pair of equations appears in [17] which contains a study of the stability of two dimensional surface waves on deep water.…”

Section: E(m)mentioning

confidence: 99%

Resonant interfacial capillary–gravity waves in the presence of damping effects

Jones

2018

European Journal of Mechanics - B/Fluids

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An investigation is made into the waves of small and moderate amplitude which may occur at the interface of two inviscid fluids of different densities. The external forces are those of gravity and surface tension and the waves are due to the resonant interaction between the Mth and Nth harmonics of the fundamental mode. In contrast to previous studies, damping effects are taken into account. Important parameters in the problem are the velocity and density ratios. A pair of coupled nonlinear Schrodinger-type partial differential equations for the wave amplitudes is derived which model the evolution of the waves, correct up to third order. A wide variety of sinusoidal solutions to the equations is shown to exist, irrespective of the values assigned to the parameters. The stability of these solutions to small modulational perturbations is considered. It is found that when the damping is due to dissipation then the waves are stabilized.

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Section: E(m)mentioning

confidence: 99%

Resonant interfacial capillary–gravity waves in the presence of damping effects

Jones

2018

European Journal of Mechanics - B/Fluids

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On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations

Jones

2024

APM

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The stability of a set of spatially constant plane wave solutions to a pair of damped coupled nonlinear Schrödinger evolution equations is considered. The equations could model physical phenomena arising in fluid dynamics, fibre optics or electron plasmas. The main result is that any small perturbation to the solution remains small for all time. Here small is interpreted as being both in the supremum sense and the square integrable sense.

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Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary–gravity waves

Abstract: Please cite this article as: M.C.W. Jones , Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary-gravity waves, Applied Mathematical Modelling (2015),

Cited by 2 publications

References 28 publications

Resonant interfacial capillary–gravity waves in the presence of damping effects

Resonant interfacial capillary–gravity waves in the presence of damping effects

On Two Types of Stability of Solutions to a Pair of Damped Coupled Nonlinear Evolution Equations

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