Free Access
Issue |
ESAIM: M2AN
Volume 34, Number 4, July/August 2000
|
|
---|---|---|
Page(s) | 873 - 911 | |
DOI | https://doi.org/10.1051/m2an:2000107 | |
Published online | 15 April 2002 |
- S. Alinhac and P. Gerard, Opérateurs pseudo-différentiels et thérorème de Nash-Moser. Interéditions/Éditions du CNRS (1991). [Google Scholar]
- 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. [Google Scholar]
- W. Ben Youssef, The global Cauchy problem for Korteweg-de Vries type systems describing counter-propagating waves. MAB, Université Bordeaux I, preprint (1999). [Google Scholar]
- 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). [Google Scholar]
- J.L. Bona and H. Chen, Lecture notes in Austin. Texas Institute for Computational and Applied Mathematics (1997). [Google Scholar]
- J.L. Bona and H. Chen, A Boussinesq system for two-way propagation of nonlinear dispersive waves. Physica D 116 (1998) 191-224. [CrossRef] [MathSciNet] [Google Scholar]
- J.L. Bona, H. Chen and J.C. Saut, personal communications. [Google Scholar]
- 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. [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- S. Cordier and E. Grenier, Quasineutral limit of Euler-Poisson system arising from plasma physics. Université de Paris VI, preprint (1997). [Google Scholar]
- 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. [Google Scholar]
- 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). [Google Scholar]
- R.K. Dodd, J.C. Eilbeck, J.D. Gibbon and H.C. Morris, Solitons and nonlinear wave equations. Academic Press (1982). [Google Scholar]
- 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). [Google Scholar]
- J.L. Joly, G. Metivier and J. Rauch, Diffractive nonlinear geometric optics with rectification. Indiana Univ. Math. J. 47 (1998) 1167-1241. [MathSciNet] [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- T. Kato, Perturbation theory for linear operators. Grundlehren Math. Wiss. 132 (1966). [Google Scholar]
- 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. [Google Scholar]
- 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. [Google Scholar]
- D. Lannes, Dispersive effects for nonlinear geometrical optics with rectification. Asymptot. Anal. 18 (1998) 111-146. [MathSciNet] [Google Scholar]
- 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). [Google Scholar]
- G.B. Whitham, Linear and nonlinear waves. J. Wiley, New York (1974). [Google Scholar]
- 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. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.