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RESEARCH PRODUCT

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

Mariana HaragusErik Wahlén

subject

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)

description

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.

yearjournalcountryeditionlanguage
2017-01-03
10.1016/j.jde.2016.11.025http://arxiv.org/abs/1604.00288