@article{M2AN_2000__34_4_873_0, author = {Ben Youssef, Walid and Colin, Thierry}, title = {Rigorous derivation of {Korteweg-de} {Vries-type} systems from a general class of nonlinear hyperbolic systems}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {873--911}, publisher = {Dunod}, address = {Paris}, volume = {34}, number = {4}, year = {2000}, mrnumber = {1784490}, zbl = {0962.35152}, language = {en}, url = {http://archive.numdam.org/item/M2AN_2000__34_4_873_0/} }
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: Modélisation mathématique et analyse numérique PY - 2000 SP - 873 EP - 911 VL - 34 IS - 4 PB - Dunod PP - Paris UR - http://archive.numdam.org/item/M2AN_2000__34_4_873_0/ LA - en ID - M2AN_2000__34_4_873_0 ER -
%0 Journal Article %A Ben Youssef, Walid %A Colin, Thierry %T Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems %J ESAIM: Modélisation mathématique et analyse numérique %D 2000 %P 873-911 %V 34 %N 4 %I Dunod %C Paris %U http://archive.numdam.org/item/M2AN_2000__34_4_873_0/ %G en %F M2AN_2000__34_4_873_0
Ben Youssef, Walid; Colin, Thierry. Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems. ESAIM: Modélisation mathématique et analyse numérique, Tome 34 (2000) no. 4, pp. 873-911. http://archive.numdam.org/item/M2AN_2000__34_4_873_0/
[1] Opérateurs pseudo-différentiels et thérorème de Nash-Moser. Interéditions/Éditions du CNRS (1991). | MR | Zbl
and ,[2] Model equations for long waves in nonlinear, dispersive Systems. Philos. Trans. Roy. Soc. Lond. A 272 (1972) 47-78. | MR | Zbl
, and ,[3] The global Cauchy problem for Korteweg-de Vries type Systems describing counter-propagating waves. MAB, Université Bordeaux I, preprint (1999).
,[4] Conservative, high order schemes and numerical study of a coupled system of Korteweg-de Vries type. Université de Bordeaux I, preprint (1999).
,[5] Lecture notes in Austin. Texas Institute for Computational and Applied Mathematics (1997).
and ,[6] A Boussinesq system for two-way propagation of nonlinear dispersive waves. Physica D 116 (1998) 191-224. | MR | Zbl
and ,[7]
, and , personal communications.[8] The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Roy. Soc. Lond. A 278 (1975) 555-604. | MR | Zbl
and ,[9] Fourier transform restriction phenomena for certain lattice substes and applications to nonlinear evolution equations. II. The Korteweg-de Vries equation. Geom. Funct. Anal. 3 (1993) 209-262. | MR | Zbl
,[10] Quasineutral limit of Euler-Poisson system arising from plasma physics. Université de Paris VI, preprint (1997). | MR | Zbl
and ,[11] An existence theory for water waves and the Boussinesq and the Korteweg-de Vries scaling limits. Comm. Partial Differential Equations 10 (1985) 787-1003. | MR | Zbl
,[12] Rigorous derivation of the nonlinear Schrodinger equation and Davey-Stewartson Systems from quadratic hyperbolic Systems. Université de Bordeaux I, preprint No. 99001 (1999). | MR | Zbl
,[13] Solitons and nonlinear wave equations. Academic Press (1982). | MR | Zbl
, , and ,[14] Diffractive nonlinear geometric optics. I. Séminaire équations aux dérivées partielles. École Polytechnique, Palaiseau, exposé No. XVII-XVIII (1995-1996). | Numdam | MR | Zbl
, , and ,[15] Diffractive nonlinear geometric optics with rectification. Indiana Univ. Math. J. 47 (1998) 1167-1241. | MR | Zbl
, and ,[16] Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Duke Math. J. 70 (1993) 373-404. | MR | Zbl
, and ,[17] Perturbation theory for linear operators. Grundlehren Math. Wiss. 132 (1966). | MR | Zbl
,[18] Well posedness and scaterring results for the generalized Korteweg-de Vries equation via the contraction principle. Comm. Pure Appl. Math. XLVI (1993) 527-620. | MR | Zbl
, and ,[19] On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary wave. Phil. Mag. 39 (1895) 422-443. | JFM
and ,[20] Dispersive effects for nonlinear geometrical optics with rectification. Asymptot. Anal. 18 (1998) 111-146. | MR | Zbl
,[21] The long wave limit for the water wave problem. I. The case of zero surface tension. University of Bayreuth, preprint (1999). | MR | Zbl
and ,[22] Linear and nonlinear waves. J. Wiley, New York (1974). | MR | Zbl
,[23] Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240.
and ,