Nonlinear Schrödinger equation with a point defect
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 5, pp. 837-845.
@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] Albeverio S., Gesztesy F., Hëgh-Krohn R., Holden H., Solvable Models in Quantum Mechanics, Springer-Verlag, New York, 1988. | MR | Zbl

[2] Berestycki H., Cazenave T., 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] Brézis H., Lieb E.H., A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR | Zbl

[4] Cazenave T., Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, American Mathematical Society, Courant Institute of Mathematical Sciences, 2003. | MR | Zbl

[5] Cazenave T., Lions P.L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys. 85 (1982) 549-561. | MR | Zbl

[6] Cid C., Felmer P., Orbital stability of standing waves for the nonlinear Schrödinger equation with potential, Rev. Math. Phys. 13 (2001) 1529-1546. | MR | Zbl

[7] Comech A., Pelinovsky D., Purely nonlinear instability of standing waves with minimal energy, Commun. Pure Appl. Math. 56 (2003) 1565-1607. | MR | Zbl

[8] De Bouard A., Fukuizumi R., Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Ann. Henri Poincaré 6 (2005) 1157-1177. | MR | Zbl

[9] Fibich G., Wang X.P., Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Physica D 175 (2003) 96-108. | MR | Zbl

[10] Fukuizumi R., Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials, Adv. Differential Equations 10 (2005) 259-276. | MR | Zbl

[11] Fukuizumi R., Ohta M., Instability of standing waves for nonlinear Schrödinger equations with potentials, Differential Integral Equations 16 (2003) 691-706. | MR | Zbl

[12] Fukuizumi R., Ohta M., Stability of standing waves for nonlinear Schrödinger equations with potentials, Differential Integral Equations 16 (2003) 111-128. | MR | Zbl

[13] Goodman R.H., Holmes P.J., Weinstein M.I., Strong NLS soliton-defect interactions, Physica D 192 (2004) 215-248. | MR | Zbl

[14] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987) 160-197. | MR | Zbl

[15] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal. 94 (1990) 308-348. | MR | Zbl

[16] Kabeya Y., Tanaka K., Uniqueness of positive radial solutions of semilinear elliptic equations in R n 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] Kunze M., Küpper T., Mezentsev V.K., Shapiro E.G., Turitsyn S., Nonlinear solitary waves with Gaussian tails, Physica D 128 (1999) 273-295. | MR | Zbl

[19] Lieb E.H., Loss M., Analysis, second ed., American Mathematical Society, 2001. | MR | Zbl

[20] Oh Y.G., Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials, Commun. Math. Phys. 121 (1989) 11-33. | MR | Zbl

[21] Ohta M., 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] Rose H.A., Weinstein M.I., On the bound states of the nonlinear Schrödinger equation with a linear potential, Physica D 30 (1988) 207-218. | MR | Zbl

[23] Shatah J., Stable standing waves of nonlinear Klein-Gordon equations, Commun. Math. Phys. 91 (1983) 313-327. | MR | Zbl

[24] Shatah J., Strauss W., Instability of nonlinear bound states, Commun. Math. Phys. 100 (1985) 173-190. | MR | Zbl

[25] Sulem C., Sulem P.-L., The Nonlinear Schrödinger Equation. Self-Focusing and Wave Collapse, Applied Mathematical Sciences, vol. 139, Springer-Verlag, New York, 1999. | MR | Zbl

[26] Weinstein M.I., Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys. 87 (1983) 567-576. | MR | Zbl

[27] Weinstein M.I., Lyapunov stability of ground states of nonlinear dispersive evolution equations, Commun. Pure Appl. Math. 39 (1986) 51-68. | MR | Zbl

[28] Zhang J., Stability of standing waves for the nonlinear Schrödinger equations with unbounded potentials, Z. Angew. Math. Phys. 51 (2000) 489-503. | MR | Zbl

[29] Zhang J., Stability of attractive Bose-Einstein condensates, J. Statist. Phys. 101 (2000) 731-745. | MR | Zbl

Cité par Sources :