Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems

Walid Ben Youssef; Thierry Colin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 4, page 873-911
  • ISSN: 0764-583X

Abstract

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In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.

How to cite

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Ben Youssef, Walid, and Colin, Thierry. "Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems." ESAIM: Mathematical Modelling and Numerical Analysis 34.4 (2010): 873-911. <http://eudml.org/doc/197564>.

@article{BenYoussef2010,
abstract = { In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type. },
author = {Ben Youssef, Walid, Colin, Thierry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Hyperbolic systems; systems of KdV-type; Euler-Poisson; water-waves; asymptotic expansion; long-wave approximation.; quasilinear symmetric hyperbolic systems; long wave limit; Euler equations; Euler-Poisson systems},
language = {eng},
month = {3},
number = {4},
pages = {873-911},
publisher = {EDP Sciences},
title = {Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems},
url = {http://eudml.org/doc/197564},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Ben Youssef, Walid
AU - Colin, Thierry
TI - Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 4
SP - 873
EP - 911
AB - In this paper, we study the long wave approximation for quasilinear symmetric hyperbolic systems. Using the technics developed by Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that under suitable assumptions the long wave limit is described by KdV-type systems. The error estimate if the system is coupled appears to be better. We apply formally our technics to Euler equations with free surface and Euler-Poisson systems. This leads to new systems of KdV-type.
LA - eng
KW - Hyperbolic systems; systems of KdV-type; Euler-Poisson; water-waves; asymptotic expansion; long-wave approximation.; quasilinear symmetric hyperbolic systems; long wave limit; Euler equations; Euler-Poisson systems
UR - http://eudml.org/doc/197564
ER -

References

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