- M.J. Ablowitz and H. Segur, On the evolution of packets of water waves. J. Fluid Mech. 92 (1979) 691–715. [CrossRef] [MathSciNet]
- 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]
- 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]
- 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]
- D.J. Benney and J.C. Luke, On the interactions of permanent waves of finite amplitude. J. Math. Phys. 43 (1964) 309–313.
- 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]
- J.L. Bona, T. Colin and D. Lannes, Long wave approximations for water waves. Preprint Université de Bordeaux I, U-03-22 (2003).
- 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]
- 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]
- 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]
- D. Lannes, Consistency of the KP approximation. Discrete Contin. Dyn. Syst. (suppl.) (2003) 517–525. Dynam. Syst. Differ. equations (Wilmington, NC, 2002).
- P.A. Milewski and J.B. Keller, Three-dimensional water waves. Stud. Appl. Math. 97 (1996) 149–166. [MathSciNet]
- 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]
- L. Paumond, Towards a rigorous derivation of the fifth order KP equation. Submitted for publication (2002).
- L. Paumond, A rigorous link between KP and a Benney-Luke equation. Differential Integral Equations 16 (2003) 1039–1064. [MathSciNet]
- R.L. Pego and J.R. Quintero, Two-dimensional solitary waves for a Benney-Luke equation. Physica D 132 (1999) 476–496. [CrossRef] [MathSciNet]
- 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]
Volume 38, Number 3, May-June 2004
|Page(s)||419 - 436|
|Published online||15 June 2004|