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. 
@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},
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     address = {Paris},
     volume = {34},
     number = {4},
     year = {2000},
     mrnumber = {1784490},
     zbl = {0962.35152},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2000__34_4_873_0/}
}
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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://www.numdam.org/item/M2AN_2000__34_4_873_0/

[1] S. Alinhac and P. Gerard, Opérateurs pseudo-différentiels et thérorème de Nash-Moser. Interéditions/Éditions du CNRS (1991). | MR | Zbl

[2] T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear, dispersive Systems. Philos. Trans. Roy. Soc. Lond. A 272 (1972) 47-78. | MR | Zbl

[3] W. Ben Youssef, The global Cauchy problem for Korteweg-de Vries type Systems describing counter-propagating waves. MAB, Université Bordeaux I, preprint (1999).

[4] W. Ben Youssef, Conservative, high order schemes and numerical study of a coupled system of Korteweg-de Vries type. Université de Bordeaux I, preprint (1999).

[5] J. L. Bona and H. Chen, Lecture notes in Austin. Texas Institute for Computational and Applied Mathematics (1997).

[6] J. L. Bona and H. Chen, A Boussinesq system for two-way propagation of nonlinear dispersive waves. Physica D 116 (1998) 191-224. | MR | Zbl

[7] J. L. Bona, H. Chen and J. C. Saut, personal communications.

[8] J. L. Bona and R. Smith, The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Roy. Soc. Lond. A 278 (1975) 555-604. | MR | Zbl

[9] J. Bourgain, 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] S. Cordier and E. Grenier, Quasineutral limit of Euler-Poisson system arising from plasma physics. Université de Paris VI, preprint (1997). | MR | Zbl

[11] W. Craig, 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] T. Colin, 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] R. K. Dodd, J. C. Eilbeck, J. D. Gibbon and H. C. Morris, Solitons and nonlinear wave equations. Academic Press (1982). | MR | Zbl

[14] P. Donnat, J. L. Joly, G. Metivier and J. Rauch, Diffractive nonlinear geometric optics. I. Séminaire équations aux dérivées partielles. École Polytechnique, Palaiseau, exposé No. XVII-XVIII (1995-1996). | Numdam | MR | Zbl

[15] J. L. Joly, G. Metivier and J. Rauch, Diffractive nonlinear geometric optics with rectification. Indiana Univ. Math. J. 47 (1998) 1167-1241. | MR | Zbl

[16] J.L. Joly, G. Metivier and J. Rauch, Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves. Duke Math. J. 70 (1993) 373-404. | MR | Zbl

[17] T. Kato, Perturbation theory for linear operators. Grundlehren Math. Wiss. 132 (1966). | MR | Zbl

[18] C.E. Kenig, G. Ponce and L. Vega, 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

[19] D.J. Korteweg and G. De Vries, 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

[20] D. Lannes, Dispersive effects for nonlinear geometrical optics with rectification. Asymptot. Anal. 18 (1998) 111-146. | MR | Zbl

[21] G. Schneider and C.E. Wayne, The long wave limit for the water wave problem. I. The case of zero surface tension. University of Bayreuth, preprint (1999). | MR | Zbl

[22] G.B. Whitham, Linear and nonlinear waves. J. Wiley, New York (1974). | MR | Zbl

[23] N.J. Zabusky and M.D. Kruskal, Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240.