Nonlinear Schrödinger equation with a point defect
Reika Fukuizumi; Masahito Ohta; Tohru Ozawa
Annales de l'I.H.P. Analyse non linéaire (2008)
- Volume: 25, Issue: 5, page 837-845
- ISSN: 0294-1449
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topFukuizumi, Reika, Ohta, Masahito, and Ozawa, Tohru. "Nonlinear Schrödinger equation with a point defect." Annales de l'I.H.P. Analyse non linéaire 25.5 (2008): 837-845. <http://eudml.org/doc/78815>.
@article{Fukuizumi2008,
author = {Fukuizumi, Reika, Ohta, Masahito, Ozawa, Tohru},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear Schrödinger equations; attractive delta-function impurity; standing wave; orbital stability},
language = {eng},
number = {5},
pages = {837-845},
publisher = {Elsevier},
title = {Nonlinear Schrödinger equation with a point defect},
url = {http://eudml.org/doc/78815},
volume = {25},
year = {2008},
}
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
PB - Elsevier
VL - 25
IS - 5
SP - 837
EP - 845
LA - eng
KW - nonlinear Schrödinger equations; attractive delta-function impurity; standing wave; orbital stability
UR - http://eudml.org/doc/78815
ER -
References
top- [1] Albeverio S., Gesztesy F., Hëgh-Krohn R., Holden H., Solvable Models in Quantum Mechanics, Springer-Verlag, New York, 1988. Zbl0679.46057MR926273
- [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. Zbl0492.35010MR646873
- [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. Zbl0526.46037MR699419
- [4] Cazenave T., Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, vol. 10, American Mathematical Society, Courant Institute of Mathematical Sciences, 2003. Zbl1055.35003MR2002047
- [5] Cazenave T., Lions P.L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys.85 (1982) 549-561. Zbl0513.35007MR677997
- [6] Cid C., Felmer P., Orbital stability of standing waves for the nonlinear Schrödinger equation with potential, Rev. Math. Phys.13 (2001) 1529-1546. Zbl1038.35112MR1869816
- [7] Comech A., Pelinovsky D., Purely nonlinear instability of standing waves with minimal energy, Commun. Pure Appl. Math.56 (2003) 1565-1607. Zbl1072.35165MR1995870
- [8] de Bouard A., Fukuizumi R., Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Ann. Henri Poincaré6 (2005) 1157-1177. Zbl1085.35123MR2189380
- [9] Fibich G., Wang X.P., Stability of solitary waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities, Physica D175 (2003) 96-108. Zbl1098.74614MR1957907
- [10] Fukuizumi R., Stability of standing waves for nonlinear Schrödinger equations with critical power nonlinearity and potentials, Adv. Differential Equations10 (2005) 259-276. Zbl1107.35100MR2123132
- [11] Fukuizumi R., Ohta M., Instability of standing waves for nonlinear Schrödinger equations with potentials, Differential Integral Equations16 (2003) 691-706. Zbl1031.35131MR1973275
- [12] Fukuizumi R., Ohta M., Stability of standing waves for nonlinear Schrödinger equations with potentials, Differential Integral Equations16 (2003) 111-128. Zbl1031.35132MR1948875
- [13] Goodman R.H., Holmes P.J., Weinstein M.I., Strong NLS soliton-defect interactions, Physica D192 (2004) 215-248. Zbl1061.35132MR2065079
- [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. Zbl0656.35122MR901236
- [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. Zbl0711.58013MR1081647
- [16] Kabeya Y., Tanaka K., Uniqueness of positive radial solutions of semilinear elliptic equations in and Séré’s non-degeneracy condition, Comm. Partial Differential Equations24 (1999) 563-598. Zbl0930.35064MR1683050
- [17] J. Holmer, J. Marzuola, M. Zworski, Fast soliton scattering by delta impurities, Preprint. Zbl1126.35068MR2318852
- [18] Kunze M., Küpper T., Mezentsev V.K., Shapiro E.G., Turitsyn S., Nonlinear solitary waves with Gaussian tails, Physica D128 (1999) 273-295. Zbl0935.35152MR1688261
- [19] Lieb E.H., Loss M., Analysis, second ed., American Mathematical Society, 2001. Zbl0966.26002MR1817225
- [20] Oh Y.G., Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials, Commun. Math. Phys.121 (1989) 11-33. Zbl0693.35132MR985612
- [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. Zbl0868.35111MR1317007
- [22] Rose H.A., Weinstein M.I., On the bound states of the nonlinear Schrödinger equation with a linear potential, Physica D30 (1988) 207-218. Zbl0694.35202MR939275
- [23] Shatah J., Stable standing waves of nonlinear Klein–Gordon equations, Commun. Math. Phys.91 (1983) 313-327. Zbl0539.35067MR723756
- [24] Shatah J., Strauss W., Instability of nonlinear bound states, Commun. Math. Phys.100 (1985) 173-190. Zbl0603.35007MR804458
- [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. Zbl0928.35157MR1696311
- [26] Weinstein M.I., Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys.87 (1983) 567-576. Zbl0527.35023MR691044
- [27] Weinstein M.I., Lyapunov stability of ground states of nonlinear dispersive evolution equations, Commun. Pure Appl. Math.39 (1986) 51-68. Zbl0594.35005MR820338
- [28] Zhang J., Stability of standing waves for the nonlinear Schrödinger equations with unbounded potentials, Z. Angew. Math. Phys.51 (2000) 489-503. Zbl0985.35085MR1762704
- [29] Zhang J., Stability of attractive Bose–Einstein condensates, J. Statist. Phys.101 (2000) 731-745. Zbl0989.82024MR1804895
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