0000000000396824

AUTHOR

Mariana Haragus

showing 2 related works from this author

Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

2017

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.

Transverse instabilitymedia_common.quotation_subjectFOS: Physical sciences35Q53 (Primary) 76B15 76B25 35B35 35P15 (Secondary)Pattern Formation and Solitons (nlin.PS)01 natural sciencesInstabilityMathematics - Analysis of PDEsgeneralized solitary wavesdispersive equationsFOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Spectral analysistransverse stability0101 mathematicsperiodic wavesNonlinear Sciences::Pattern Formation and SolitonsMathematical Physicsmedia_commonPhysicsApplied Mathematics010102 general mathematicsMathematical analysisOrder (ring theory)Mathematical Physics (math-ph)InfinityNonlinear Sciences - Pattern Formation and Solitons010101 applied mathematicsClassical mechanicsNonlinear Sciences::Exactly Solvable and Integrable SystemsLine (geometry)Mechanical waveAnalysisLongitudinal waveAnalysis of PDEs (math.AP)
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Numerical study of the stability of the Peregrine solution

2017

International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.

PhysicsRogue wavesGeneral Medicine01 natural sciencesStability (probability)010305 fluids & plasmasDeep waterSchrödinger equationsymbols.namesakeNonlinear systemClassical mechanics[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]Peregrine solution0103 physical sciencessymbolsNonlinear Schrödinger equation[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Rogue wave010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsNonlinear Schrödinger equationSchrödinger's cat
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