@article{AIHPC_2008__25_5_837_0, author = {Fukuizumi, Reika and Ohta, Masahito and Ozawa, Tohru}, title = {Nonlinear {Schr\"odinger} equation with a point defect}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {837--845}, publisher = {Elsevier}, volume = {25}, number = {5}, year = {2008}, doi = {10.1016/j.anihpc.2007.03.004}, mrnumber = {2457813}, zbl = {1145.35457}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2007.03.004/} }
TY - JOUR AU - Fukuizumi, Reika AU - Ohta, Masahito AU - Ozawa, Tohru TI - Nonlinear Schrödinger equation with a point defect JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 837 EP - 845 VL - 25 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2007.03.004/ DO - 10.1016/j.anihpc.2007.03.004 LA - en ID - AIHPC_2008__25_5_837_0 ER -
%0 Journal Article %A Fukuizumi, Reika %A Ohta, Masahito %A Ozawa, Tohru %T Nonlinear Schrödinger equation with a point defect %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 837-845 %V 25 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2007.03.004/ %R 10.1016/j.anihpc.2007.03.004 %G en %F AIHPC_2008__25_5_837_0
Fukuizumi, Reika; Ohta, Masahito; Ozawa, Tohru. Nonlinear Schrödinger equation with a point defect. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 5, pp. 837-845. doi : 10.1016/j.anihpc.2007.03.004. http://www.numdam.org/articles/10.1016/j.anihpc.2007.03.004/
[1] Solvable Models in Quantum Mechanics, Springer-Verlag, New York, 1988. | MR | Zbl
, , , ,[2] Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sci. Paris. 293 (1981) 489-492. | MR | Zbl
, ,[3] A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR | Zbl
, ,[4] Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, American Mathematical Society, Courant Institute of Mathematical Sciences, 2003. | MR | Zbl
,[5] Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys. 85 (1982) 549-561. | MR | Zbl
, ,[6] Orbital stability of standing waves for the nonlinear Schrödinger equation with potential, Rev. Math. Phys. 13 (2001) 1529-1546. | MR | Zbl
, ,[7] Purely nonlinear instability of standing waves with minimal energy, Commun. Pure Appl. Math. 56 (2003) 1565-1607. | MR | Zbl
, ,[8] Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Ann. Henri Poincaré 6 (2005) 1157-1177. | MR | Zbl
, ,[9] Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Physica D 175 (2003) 96-108. | MR | Zbl
, ,[10] Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials, Adv. Differential Equations 10 (2005) 259-276. | MR | Zbl
,[11] Instability of standing waves for nonlinear Schrödinger equations with potentials, Differential Integral Equations 16 (2003) 691-706. | MR | Zbl
, ,[12] Stability of standing waves for nonlinear Schrödinger equations with potentials, Differential Integral Equations 16 (2003) 111-128. | MR | Zbl
, ,[13] Strong NLS soliton-defect interactions, Physica D 192 (2004) 215-248. | MR | Zbl
, , ,[14] Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987) 160-197. | MR | Zbl
, , ,[15] Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal. 94 (1990) 308-348. | MR | Zbl
, , ,[16] Uniqueness of positive radial solutions of semilinear elliptic equations in and Séré’s non-degeneracy condition, Comm. Partial Differential Equations 24 (1999) 563-598. | MR | Zbl
, ,[17] J. Holmer, J. Marzuola, M. Zworski, Fast soliton scattering by delta impurities, Preprint. | MR
[18] Nonlinear solitary waves with Gaussian tails, Physica D 128 (1999) 273-295. | MR | Zbl
, , , , ,[19] Analysis, second ed., American Mathematical Society, 2001. | MR | Zbl
, ,[20] Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials, Commun. Math. Phys. 121 (1989) 11-33. | MR | Zbl
,[21] Stability and instability of standing waves for one dimensional nonlinear Schrödinger equations with double power nonlinearity, Kodai Math. J. 18 (1995) 68-74. | MR | Zbl
,[22] On the bound states of the nonlinear Schrödinger equation with a linear potential, Physica D 30 (1988) 207-218. | MR | Zbl
, ,[23] Stable standing waves of nonlinear Klein-Gordon equations, Commun. Math. Phys. 91 (1983) 313-327. | MR | Zbl
,[24] Instability of nonlinear bound states, Commun. Math. Phys. 100 (1985) 173-190. | MR | Zbl
, ,[25] The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Applied Mathematical Sciences, vol. 139, Springer-Verlag, New York, 1999. | MR | Zbl
, ,[26] Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys. 87 (1983) 567-576. | MR | Zbl
,[27] Lyapunov stability of ground states of nonlinear dispersive evolution equations, Commun. Pure Appl. Math. 39 (1986) 51-68. | MR | Zbl
,[28] Stability of standing waves for the nonlinear Schrödinger equations with unbounded potentials, Z. Angew. Math. Phys. 51 (2000) 489-503. | MR | Zbl
,[29] Stability of attractive Bose-Einstein condensates, J. Statist. Phys. 101 (2000) 731-745. | MR | Zbl
,Cité par Sources :