# 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

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topBen 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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