@article{AIHPC_2009__26_6_2211_0, author = {Colin, M. and Colin, Th. and Ohta, M.}, title = {Stability of {Solitary} {Waves} for a {System} of {Nonlinear} {Schr\"odinger} {Equations} {With} {Three} {Wave} {Interaction}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {2211--2226}, publisher = {Elsevier}, volume = {26}, number = {6}, year = {2009}, doi = {10.1016/j.anihpc.2009.01.011}, mrnumber = {2569892}, zbl = {1180.35478}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.011/} }
TY - JOUR AU - Colin, M. AU - Colin, Th. AU - Ohta, M. TI - Stability of Solitary Waves for a System of Nonlinear Schrödinger Equations With Three Wave Interaction JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 2211 EP - 2226 VL - 26 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.011/ DO - 10.1016/j.anihpc.2009.01.011 LA - en ID - AIHPC_2009__26_6_2211_0 ER -
%0 Journal Article %A Colin, M. %A Colin, Th. %A Ohta, M. %T Stability of Solitary Waves for a System of Nonlinear Schrödinger Equations With Three Wave Interaction %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 2211-2226 %V 26 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.011/ %R 10.1016/j.anihpc.2009.01.011 %G en %F AIHPC_2009__26_6_2211_0
Colin, M.; Colin, Th.; Ohta, M. Stability of Solitary Waves for a System of Nonlinear Schrödinger Equations With Three Wave Interaction. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2211-2226. doi : 10.1016/j.anihpc.2009.01.011. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.011/
[1] Instabilité Des États Stationnaires Dans Les Équations De Schrödinger Et De Klein-Gordon Non Linéaires, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981) 489-492. | MR | Zbl
, ,[2] Semilinear Schrödinger Equations, Courant Lect. Notes Math. 10, Amer. Math. Soc., 2003. | MR | Zbl
,[3] Orbital Stability of Standing Waves for Some Nonlinear Schrödinger Equations, Comm. Math. Phys. 85 (1982) 549-561. | MR | Zbl
, ,[4] Spectra of Linearized Operators for NLS Solitary Waves, SIAM J. Math. Anal. 39 (2007/2008) 1070-1111. | MR | Zbl
, , , ,[5] On a Quasi-Linear Zakharov System Describing Laser-Plasma Interactions, Differential Integral Equations 17 (2004) 297-330. | MR | Zbl
, ,[6] A Numerical Model for the Raman Amplification for Laser-Plasma Interaction, J. Comput. Appl. Math. 193 (2006) 535-562. | MR | Zbl
, ,[7] Instability of Stationary Bubbles, SIAM J. Math. Anal. 26 (1995) 566-582. | MR | Zbl
,[8] The Black Solitons of One-Dimensional NLS Equations, Nonlinearity 20 (2007) 461-496. | MR | Zbl
, ,[9] Nonlinear Bound States Outside an Insulated Sphere, Comm. Partial Differential Equations 19 (1994) 177-197. | MR | Zbl
, ,[10] Remarks on the Stable Standing Waves for Nonlinear Schrödinger Equations With Double Power Nonlinearity, Adv. Math. Sci. Appl. 13 (2003) 549-564. | MR | Zbl
,[11] A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schrödinger Equations, Indiana Univ. Math. J. 49 (2000) 221-243. | MR | Zbl
, , , ,[12] Stability Theory of Solitary Waves in the Presence of Symmetry, I, J. Funct. Anal. 74 (1987) 160-197. | MR | Zbl
, , ,[13] Stability Theory of Solitary Waves in the Presence of Symmetry, II, J. Funct. Anal. 94 (1990) 308-348. | MR | Zbl
, , ,[14] Stability and Instability of Solitary Waves for One-Dimensional Singular Schrödinger Equations, Differential Integral Equations 6 (1993) 685-703. | MR | Zbl
, ,[15] Uniqueness of Positive Solutions of in , Arch. Ration. Mech. Anal. 105 (1989) 234-266. | MR | Zbl
,[16] Analysis, Grad. Stud. Math., vol. 14, second ed., Amer. Math. Soc., 2001. | MR | Zbl
, ,[17] A Remark on Linearly Unstable Standing Wave Solutions to NLS, Nonlinear Anal. 64 (2006) 657-676. | MR | Zbl
,[18] Instability of Nonlinear Bound States, Comm. Math. Phys. 100 (1985) 173-190. | MR | Zbl
, ,[19] Spectral Condition for Instability, in: Contemp. Math., vol. 255, 2000, pp. 189-198. | MR | Zbl
, ,[20] The Nonlinear Schrödinger Equation: Self-Focusing and Wave-Collapse, Appl. Math. Sci., vol. 139, Springer-Verlag, 1999. | MR | Zbl
, ,[21] Lyapunov Stability of Ground States of Nonlinear Dispersive Evolution Equations, Comm. Pure Appl. Math. 39 (1986) 51-68. | MR | Zbl
,[22] Modulational Stability of Ground States of Nonlinear Schrödinger Equations, SIAM J. Math. Anal. 16 (1985) 472-491. | MR | Zbl
,Cité par Sources :