Free Access
Issue
ESAIM: M2AN
Volume 38, Number 3, May-June 2004
Page(s) 419 - 436
DOI https://doi.org/10.1051/m2an:2004020
Published online 15 June 2004
  1. M.J. Ablowitz and H. Segur, On the evolution of packets of water waves. J. Fluid Mech. 92 (1979) 691–715. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.C. Alexander, R.L. Pego and R.L. Sachs, On the transverse instability of solitary waves in the Kadomtsev-Petviashvili equation. Phys. Lett. A 226 (1997) 187–192. [CrossRef] [MathSciNet] [Google Scholar]
  3. W. Ben Youssef and T. Colin, Rigorous derivation of Korteweg-de Vries-type systems from a general class of nonlinear hyperbolic systems. ESAIM: M2AN 34 (2000) 873–911. [CrossRef] [EDP Sciences] [Google Scholar]
  4. W. Ben Youssef and D. Lannes, The long wave limit for a general class of 2D quasilinear hyperbolic problems. Comm. Partial Differ. Equations 27 (2002) 979–1020. [CrossRef] [Google Scholar]
  5. D.J. Benney and J.C. Luke, On the interactions of permanent waves of finite amplitude. J. Math. Phys. 43 (1964) 309–313. [Google Scholar]
  6. K.M. Berger and P.A. Milewski, The generation and evolution of lump solitary waves in surface-tension-dominated flows. SIAM J. Appl. Math. 61 (2002) 731–750 (electronic). [CrossRef] [Google Scholar]
  7. J.L. Bona, T. Colin and D. Lannes, Long wave approximations for water waves. Preprint Université de Bordeaux I, U-03-22 (2003). [Google Scholar]
  8. W. Craig, An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Comm. Partial Differ. Equations 10 (1985) 787–1003. [CrossRef] [MathSciNet] [Google Scholar]
  9. T. Gallay and G. Schneider, KP description of unidirectional long waves. The model case. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 885–898. [CrossRef] [MathSciNet] [Google Scholar]
  10. T. Kano and T. Nishida, A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves. Osaka J. Math. 23 (1986) 389–413. [MathSciNet] [Google Scholar]
  11. D. Lannes, Consistency of the KP approximation. Discrete Contin. Dyn. Syst. (suppl.) (2003) 517–525. Dynam. Syst. Differ. equations (Wilmington, NC, 2002). [Google Scholar]
  12. P.A. Milewski and J.B. Keller, Three-dimensional water waves. Stud. Appl. Math. 97 (1996) 149–166. [MathSciNet] [Google Scholar]
  13. P.A. Milewski and E.G. Tabak, A pseudospectral procedure for the solution of nonlinear wave equations with examples from free-surface flows. SIAM J. Sci. Comput. 21 (1999) 1102–1114 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Paumond, Towards a rigorous derivation of the fifth order KP equation. Submitted for publication (2002). [Google Scholar]
  15. L. Paumond, A rigorous link between KP and a Benney-Luke equation. Differential Integral Equations 16 (2003) 1039–1064. [MathSciNet] [Google Scholar]
  16. R.L. Pego and J.R. Quintero, Two-dimensional solitary waves for a Benney-Luke equation. Physica D 132 (1999) 476–496. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Schneider and C.E. Wayne, The long-wave limit for the water wave problem. I. The case of zero surface tension. Comm. Pure Appl. Math. 53 (2000) 1475–1535. [CrossRef] [MathSciNet] [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.

Recommended for you