Numerical study of oscillatory regimes in the kadomtsev-petviashvili equation

Christian Klein; Christof Sparber; Peter Markowich

doi:10.1007/s00332-007-9001-y

Numerical study of oscillatory regimes in the kadomtsev-petviashvili equation

Christian Klein^*, Christof Sparber, Peter Markowich

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

59 Scopus citations

Abstract

The aim of this paper is the accurate numerical study of the Kadomtsev-Petviashvili (KP) equation. In particular, we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end, we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step, we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.

Original language	English (US)
Pages (from-to)	429-470
Number of pages	42
Journal	Journal of Nonlinear Science
Volume	17
Issue number	5
DOIs	https://doi.org/10.1007/s00332-007-9001-y
State	Published - Oct 2007
Externally published	Yes

Keywords

Davey-Stewartson system
Kadomtsev-Petviashvili equation
Modulation theory
Multiple scales expansion
Nonlinear dispersive models

ASJC Scopus subject areas

Modeling and Simulation
General Engineering
Applied Mathematics

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10.1007/s00332-007-9001-y

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title = "Numerical study of oscillatory regimes in the kadomtsev-petviashvili equation",

abstract = "The aim of this paper is the accurate numerical study of the Kadomtsev-Petviashvili (KP) equation. In particular, we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end, we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step, we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.",

keywords = "Davey-Stewartson system, Kadomtsev-Petviashvili equation, Modulation theory, Multiple scales expansion, Nonlinear dispersive models",

author = "Christian Klein and Christof Sparber and Peter Markowich",

note = "Funding Information: Acknowledgements We thank B. Dubrovin, E. Ferapontov, J. Frauendiener, and T. Grava for helpful discussions and hints. This work has been supported by the Wittgenstein Award 2000 of the third author. C.S. has been supported by the APART research grant funded by the Austrian Academy of Sciences. C.K. thanks for financial support by the MISGAM program of the European Science Foundation.",

year = "2007",

month = oct,

doi = "10.1007/s00332-007-9001-y",

language = "English (US)",

volume = "17",

pages = "429--470",

journal = "Journal of Nonlinear Science",

issn = "0938-8974",

publisher = "Springer Verlag",

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TY - JOUR

T1 - Numerical study of oscillatory regimes in the kadomtsev-petviashvili equation

AU - Klein, Christian

AU - Sparber, Christof

AU - Markowich, Peter

N1 - Funding Information: Acknowledgements We thank B. Dubrovin, E. Ferapontov, J. Frauendiener, and T. Grava for helpful discussions and hints. This work has been supported by the Wittgenstein Award 2000 of the third author. C.S. has been supported by the APART research grant funded by the Austrian Academy of Sciences. C.K. thanks for financial support by the MISGAM program of the European Science Foundation.

PY - 2007/10

Y1 - 2007/10

N2 - The aim of this paper is the accurate numerical study of the Kadomtsev-Petviashvili (KP) equation. In particular, we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end, we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step, we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.

AB - The aim of this paper is the accurate numerical study of the Kadomtsev-Petviashvili (KP) equation. In particular, we are concerned with the small dispersion limit of this model, where no comprehensive analytical description exists so far. To this end, we first study a similar highly oscillatory regime for asymptotically small solutions, which can be described via the Davey-Stewartson system. In a second step, we investigate numerically the small dispersion limit of the KP model in the case of large amplitudes. Similarities and differences to the much better studied Korteweg-de Vries situation are discussed as well as the dependence of the limit on the additional transverse coordinate.

KW - Davey-Stewartson system

KW - Kadomtsev-Petviashvili equation

KW - Modulation theory

KW - Multiple scales expansion

KW - Nonlinear dispersive models

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U2 - 10.1007/s00332-007-9001-y

DO - 10.1007/s00332-007-9001-y

M3 - Article

AN - SCOPUS:84867922204

SN - 0938-8974

VL - 17

SP - 429

EP - 470

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 5

ER -

Numerical study of oscillatory regimes in the kadomtsev-petviashvili equation

Abstract

Keywords

ASJC Scopus subject areas

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