Dromion perturbation for the davey-stewartson-1 equations

Journal of Nonlinear Mathematical Physics

Volumn 7, Issue 4, 2000, Pages 411-422

  Kiselev, O M ^a  

^a INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034550820     PISSN: 14029251     EISSN: 17760852     Source Type: Journal    
DOI: 10.2991/jnmp.2000.7.4.1     Document Type: Article

References (19)

1. Davey, A., and Stewartson, K., 1974. On the Three-Dimensional Packets of Surface Waves. Proc. R. Soc. London Ser. A, 338:101–110.
2. Djordjevic, V.D., and Redekopp, L.G., 1977. On Two-Dimensional Packets of Capillary- Gravity Waves. J. Fluid Mech., 79:703–714.
3. Ghidaglia, J.-M., and Saut, J.-K., 1990. On the Initial Value Problem for the Davey-Stewartson Systems. Nonlinearity, 3:475–506.
4. Shakir’yanov, M.M., 1994. “Solvability of the Initial-Boundary Problem for the Davey-Stewartson Type System of Equations”. In Integrability in the Dynamical Systems, Inst. of Math. Ufa 49–61.
5. Nizhnik, L.P., 1991. Inverse Problems for Hyperbolic Equations, Kiev:Naukova Dumka.
6. Fokas, A.S., and Ablowitz, M.J., 1984. On the Inverse Scattering Transform of Multidimensional Non-linear Equations Related to First-Order Systems in the Plane. J. Math. Phys., 25:2494–2505.
7. Fokas, A.S., and Santini, P.M., 1990. Dromions and a Boundary Value Problem For the Davey-Stewartson I Equation. Physica D, 44:99–130.
8. Fokas, A.S., and Sung, L.J., 1992. On the Solvability on the N-Wave, Davey-Stewartson and Kadomtsev-Petviashvili Equations. Inv. probl., 8:673–708.
9. Boiti, M., Leon, J., Martina, L., and Pempinelli, F., 1988. Scattering of Localized Solitons in the Plane. Phys. Lett. A, 132:432–439.
10. Kiselev, O.M., 1997. Asymptotic Behavior of Solitonless Solution of the Davey-Stewartson-2 Equation. Differentsial’nye Uravneniya, 33:812–819.
11. Kiselev, O.M., 1998. An Asymptotic Solution of the Cauchy Problem for the Davey-Stewartson-1 Equation. Teor. Matem. Fiz., 114:104–114.
12. Nakao, H., and Hirata, H., 1996. Global Existence and Asymptotic Behavior in Time of Small Solutions to the Elliptic-Hyperbolic Davey-Stewartson System. Nonlinearity, 9:1387–1409.
13. Gadyl’shyn, R.R., and Kiselev, O.M., 1996. On Nonsoliton Structure of Scattering Data under Perturbation of Two-Dimensional Soliton for Davey-Stewartson Equation II. Teor. Matem. Fiz., 106:167–173.
14. Gadylshin, R.R., and Kiselev, O.M., 1999. Structural Instability of Soliton for Davey-Stewartson II Equation. Teor. Matem. Fiz., 118:354–361.
15. Kaup, D.J., 1976. Closure of the Squared Zakharov-Shabat Eigenstates. J. of Math. Anal. and Appl., 54:849–864.
16. Kiselev, O.M., 1998. Perturbation Theory for the Dirac Equation in Two-Dimensional Space. J. Math. Phys., 39:2333–2345.
17. Kiselev, O.M., 1998. Basic Functions Associated With Two Dimensional Dirac System. Func. Anal. Appl., 32:56–59.
18. Papanicolaou, G.S., Sulem, C., Sulem, P.L., and Wang, X.P., 1994. The Focusing Singularity of the Davey-Stewartson Equations for Gravity-Capillary Surface Waves. Physica D, 72:61–86.
19. Pelinovsky, D., 1999. Private Communication