6533b82cfe1ef96bd128ffe6

RESEARCH PRODUCT

Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves

Tamara GravaChristian KleinGiuseppe Pitton

subject

Shock waveBreatherGeneral MathematicsGeneral Physics and AstronomySemiclassical physicsFOS: Physical sciencesPattern Formation and Solitons (nlin.PS)Kadomtsev–Petviashvili equation01 natural sciences010305 fluids & plasmassymbols.namesakeMathematics - Analysis of PDEs[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]0103 physical sciencesModulation (music)FOS: Mathematics[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Mathematics - Numerical Analysis0101 mathematicsSettore MAT/07 - Fisica MatematicaNonlinear Schrödinger equationNonlinear Sciences::Pattern Formation and SolitonsLine (formation)PhysicsKadomtsev-Petviashvili equationKadomtsev Petviashvili equatuonNonlinear Sciences - Exactly Solvable and Integrable SystemsDispersive Shock waves010102 general mathematicsGeneral EngineeringNumerical Analysis (math.NA)Dispersive shock waves[ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA]Whitham equationsNonlinear Sciences - Pattern Formation and SolitonsLumpsKadomtsev Petviashvili equation dispersive shock wavesClassical mechanicsNonlinear Sciences::Exactly Solvable and Integrable SystemssymbolsSolitonExactly Solvable and Integrable Systems (nlin.SI)[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]Kadomtsev Petviashvili equationAnalysis of PDEs (math.AP)

description

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrodinger equation in the semiclassical limit.

yearjournalcountryeditionlanguage
2018-02-14
https://hal.archives-ouvertes.fr/hal-01757833