Free Access
Issue
ESAIM: M2AN
Volume 38, Number 6, November-December 2004
Page(s) 1035 - 1054
DOI https://doi.org/10.1051/m2an:2004049
Published online 15 December 2004
  1. M.J. Ablowitz and P.A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering. Cambridge University Press, London Math. Soc. Lect. Note Series 149 (1991). [Google Scholar]
  2. M.J. Ablowitz and H. Segur, Solitons and the inverse scattering transform. SIAM Stud. Appl. Math., SIAM, Philadelphia 4 (1981). [Google Scholar]
  3. V.A. Arkadiev, A.K. Pogrebkov and M.C. Polivanov, Inverse scattering transform method and soliton solutions for the Davey-Stewartson II equation. Physica D 36 (1989) 189–196. [CrossRef] [MathSciNet] [Google Scholar]
  4. W. Bao, S. Jin and P.A. Markowich, Time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. J. Comp. Phys. 175 (2002) 487–524. [Google Scholar]
  5. W. Bao, N.J. Mauser and H.P. Stimming, Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-Xα model. CMS 1 (2003) 809–831. [Google Scholar]
  6. C. Besse, Schéma de relaxation pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson. C. R. Acad. Sci. Paris I 326 (1998) 1427–1432. [Google Scholar]
  7. C. Besse and C.H. Bruneau, Numerical study of elliptic-hyperbolic Davey-Stewartson system: dromions simulation and blow-up. Math. Mod. Meth. Appl. Sci. 8 (1998) 1363–1386. [Google Scholar]
  8. C. Besse, B. Bidégaray and S. Descombes, Order estimates in time of the splitting methods for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 40 (2002) 26–40. [CrossRef] [MathSciNet] [Google Scholar]
  9. S. Descombes, Convergence of a splitting method of high order for reaction-diffusion systems. Math. Comp. 70 (2001) 1481–1501. [CrossRef] [MathSciNet] [Google Scholar]
  10. V.D. Djordjević and L.G. Redekopp, On two-dimensional packets of capillary-gravity waves. J. Fluid Mech. 79 (1977) 703–714. [CrossRef] [MathSciNet] [Google Scholar]
  11. J.M. Ghidaglia and J.C. Saut, On the initial value problem for the Davey-Stewartson systems. Nonlinearity 3 (1990) 475–506. [CrossRef] [MathSciNet] [Google Scholar]
  12. M. Guzmán-Gomez, Asymptotic behaviour of the Davey-Stewartson system. C. R. Math. Rep. Acad. Sci. Canada 16 (1994) 91–96. [MathSciNet] [Google Scholar]
  13. R.H. Hardin and F.D. Tappert, Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations. SIAM Rev. Chronicle 15 (1973) 423. [Google Scholar]
  14. N. Hayashi, Local existence in time solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data. J. Anal. Math. LXXIII (1997) 133–164. [Google Scholar]
  15. N. Hayashi and H. Hirata, Global existence and asymptotic behaviour of small solutions to the elliptic-hyperbolic Davey-Stewartson system. Nonlinearity 9 (1996) 1387–1409. [CrossRef] [MathSciNet] [Google Scholar]
  16. N. Hayashi and J.C. Saut, Global existence of small solutions to the Davey-Stewartson and Ishimori systems. Diff. Int. Eq. 8 (1995) 1657–1675. [Google Scholar]
  17. M.J. Landman, G.C. Papanicolaou, C. Sulem and P.-L. Sulem, Rate of blowup for solutions of the Nonlinear Schrödinger equation at critical dimension. Phys. Rev. A 38 (1988) 3837–3843. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  18. F. Merle, Construction of solutions with exactly k blowup points for the Schrödinger equation with critical nonlinearity. Comm. Math. Phys. 129 (1990) 223–240. [CrossRef] [MathSciNet] [Google Scholar]
  19. K. Nishinari, K. Abe and J. Satsuma, Multidimensional behaviour of an electrostatic ion wave in a magnetized plasma. Phys. Plasmas 1 (1994) 2559–2565. [CrossRef] [Google Scholar]
  20. T. Ozawa, Exact blow-up solutions to the Cauchy problem for the Davey-Stewartson systems. Proc. R. Soc. A 436 (1992) 345–349. [CrossRef] [Google Scholar]
  21. G.C. Papanicolaou, C. Sulem, P.-L. Sulem, X.P. Wang, The focusing singularity of the Davey-Stewartson equations for gravity-capillary surface waves. Physica D 72 (1994) 61–86. [CrossRef] [MathSciNet] [Google Scholar]
  22. C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse. Springer, New York (1999) [Google Scholar]
  23. P.W. White and J.A.C. Weideman, Numerical simulation of solitons and dromions in the Davey-Stewartson system. Math. Comput. Simul. 37 (1994) 469–479. [CrossRef] [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