-
1
-
-
0000127687
-
Self-focusing of optical beams
-
Kelley P L 1965 Self-focusing of optical beams Phys. Rev. Lett. 15 1005-8
-
(1965)
Phys. Rev. Lett.
, vol.15
, pp. 1005-1008
-
-
Kelley, P.L.1
-
2
-
-
84990553632
-
On uniqueness and continuation properties after blow-up time of self-similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass
-
Merle F 1992 On uniqueness and continuation properties after blow-up time of self-similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass Commun. Pure Appl. Math. 45 203-54
-
(1992)
Commun. Pure Appl. Math.
, vol.45
, pp. 203-254
-
-
Merle, F.1
-
3
-
-
21144476343
-
Limit behavior of saturated approximations of nonlinear Schrödinger equation
-
Merle F 1992 Limit behavior of saturated approximations of nonlinear Schrödinger equation Commun. Math. Phys. 149 377-414
-
(1992)
Commun. Math. Phys.
, vol.149
, pp. 377-414
-
-
Merle, F.1
-
5
-
-
79959252167
-
Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equation
-
Tao T 2009 Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equation Anal. PDE 2 61-81
-
(2009)
Anal. PDE
, vol.2
, pp. 61-81
-
-
Tao, T.1
-
7
-
-
0000246714
-
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
-
Bourgain J and Wang W 1997 Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity Ann. Scuola Norm. Sup. Pisa Cl. Sci. 25 197-215
-
(1997)
Ann. Scuola Norm. Sup. Pisa Cl. Sci.
, vol.25
, pp. 197-215
-
-
Bourgain, J.1
Wang, W.2
-
8
-
-
0001145199
-
On the analytical theory for stationary self-focusing of radiation
-
Malkin V 1993 On the analytical theory for stationary self-focusing of radiation Physica D 64 251-66
-
(1993)
Physica
, vol.64
, pp. 251-266
-
-
Malkin, V.1
-
9
-
-
0342647291
-
Self-focusing in the perturbed and unperturbed nonlinear Schrodinger equation in critical dimension
-
Fibich G and Papanicolaou G C 1999 Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension SIAM Appl. Math. 60 183-240 (Pubitemid 30581050)
-
(2000)
SIAM Journal on Applied Mathematics
, vol.60
, Issue.1
, pp. 183-240
-
-
Fibich, G.1
Papanicolaou, G.2
-
11
-
-
0003482633
-
-
(Providence, RI: American Mathematical Society)
-
Strauss W 1989 Nonlinear Wave Equation (Providence, RI: American Mathematical Society)
-
(1989)
Nonlinear Wave Equation
-
-
Strauss, W.1
-
12
-
-
0041473959
-
Nonlinear Schrödinger equations and sharp interpolation estimates
-
Weinstein M I 1983 Nonlinear Schrödinger equations and sharp interpolation estimates Commun. Math. Phys. 87 567-76
-
(1983)
Commun. Math. Phys.
, vol.87
, pp. 567-576
-
-
Weinstein, M.I.1
-
13
-
-
0041350485
-
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
-
DOI 10.1007/s00039-003-0424-9
-
Merle F and Raphael P 2003 Sharp upper bound on the blowup rate for the critical nonlinear Schrödinger equation Geom. Funct. Anal. 13 591-642 (Pubitemid 37049166)
-
(2003)
Geometric and Functional Analysis
, vol.13
, Issue.3
, pp. 591-642
-
-
Merle, F.1
Raphael, P.2
-
14
-
-
2942586742
-
2 critical nonlinear Schrödinger equation
-
DOI 10.1007/s00222-003-0346-z
-
2 critical nonlinear Schrödinger equation Invent. Math. 156 565-672 (Pubitemid 38739738)
-
(2004)
Inventiones Mathematicae
, vol.156
, Issue.3
, pp. 565-672
-
-
Merle, F.1
Raphael, P.2
-
15
-
-
20444437961
-
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
-
Merle F and Raphael P 2005 Blow-up dynamics and upper bound on the blow-up rate for the critical nonlinear Schrödinger equation Ann. Math. 161 157-222 (Pubitemid 41137799)
-
(2005)
Annals of Mathematics
, vol.161
, Issue.1
, pp. 157-222
-
-
Merle, F.1
Raphael, P.2
-
16
-
-
12444281836
-
Profiles and quantization of the blow-up mass for critical nonlinear Schrödinger equation
-
Merle F and Raphael P 2005 Profiles and quantization of the blow-up mass for critical nonlinear Schrödinger equation Commun. Math. Phys. 253 675-704
-
(2005)
Commun. Math. Phys.
, vol.253
, pp. 675-704
-
-
Merle, F.1
Raphael, P.2
-
18
-
-
34547283966
-
On one blow up point solutions to the critical nonlinear Schrödinger equation
-
Merle F and Raphael P 2005 On one blow up point solutions to the critical nonlinear Schrödinger equation J. Hyperbolic Differ. Eqns 2 919-62
-
(2005)
J. Hyperbolic Differ. Eqns
, vol.2
, pp. 919-962
-
-
Merle, F.1
Raphael, P.2
-
19
-
-
13844296411
-
Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation
-
DOI 10.1007/s00208-004-0596-0
-
Raphael P 2005 Stability of the log-log bound for blow up solutions to the critical non linear Schrödinger equation Math. Ann. 331 577-609 (Pubitemid 40251235)
-
(2005)
Mathematische Annalen
, vol.331
, Issue.3
, pp. 577-609
-
-
Raphael, P.1
-
20
-
-
0001678668
-
Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
-
LeMesurier B, Sulem C, Papanicolaou G and Sulem P L 1988 Local structure of the self-focusing singularity of the nonlinear Schrödinger equation Physica D 32 210-26
-
(1988)
Physica
, vol.32
, pp. 210-226
-
-
Lemesurier, B.1
Sulem, C.2
Papanicolaou, G.3
Sulem, P.L.4
-
21
-
-
0000893351
-
Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
-
Landman M, Papanicolaou G, Sulem C and Sulem P L 1988 Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension Phys. Rev. A 38 3837-43
-
(1988)
Phys. Rev.
, vol.38
, pp. 3837-3843
-
-
Landman, M.1
Papanicolaou, G.2
Sulem, C.3
Sulem, P.L.4
-
22
-
-
0000548165
-
Asymptotic stability of manifold of self-similar solutions in self-focusing
-
Fraiman G 1985 Asymptotic stability of manifold of self-similar solutions in self-focusing Sov. Phys. JETP 61 228-33
-
(1985)
Sov. Phys. JETP
, vol.61
, pp. 228-233
-
-
Fraiman, G.1
-
24
-
-
27644512464
-
New singular solutions of the nonlinear Schrödinger equation
-
DOI 10.1016/j.physd.2005.08.007, PII S0167278905003520
-
Fibich G, Gavish N and Wang X P 2005 New singular solutions of the nonlinear Schrödinger equation Physica D 211 193-220 (Pubitemid 41550113)
-
(2005)
Physica D: Nonlinear Phenomena
, vol.211
, Issue.3-4
, pp. 193-220
-
-
Fibich, G.1
Gavish, N.2
Wang, X.-P.3
-
25
-
-
34249993538
-
Singular ring solutions of critical and supercritical nonlinear Schrödinger equations
-
DOI 10.1016/j.physd.2007.04.007, PII S0167278907001297
-
Fibich G, Gavish N and Wang X P 2007 Singular ring solutions of critical and supercritical nonlinear Schrödinger equations Physica D 231 55-86 (Pubitemid 46891621)
-
(2007)
Physica D: Nonlinear Phenomena
, vol.231
, Issue.1
, pp. 55-86
-
-
Fibich, G.1
Gavish, N.2
Wang, X.-P.3
-
26
-
-
77956095269
-
Singular standing ring solutions of nonlinear partial differential equations
-
Baruch G, Fibich G and Gavish N 2010 Singular standing ring solutions of nonlinear partial differential equations Physica D 239 1968-83
-
(2010)
Physica
, vol.239
, pp. 1968-1983
-
-
Baruch, G.1
Fibich, G.2
Gavish, N.3
-
27
-
-
0442279560
-
Three-dimension simulation of jet formation in collapsing condensates
-
Bao W, Jaksch D and Markowich P A 2004 Three-dimension simulation of jet formation in collapsing condensates J. Phys. B: At. Mol. Opt. Phys. 37 329-43
-
(2004)
J. Phys. B: At. Mol. Opt. Phys.
, vol.37
, pp. 329-343
-
-
Bao, W.1
Jaksch, D.2
Markowich, P.A.3
-
28
-
-
0035183227
-
Self-focusing in the damped nonlinear Schrödinger equation
-
DOI 10.1137/S0036139999362609, PII S0036139999362609
-
Fibich G 2001 Self-focusing in the damped nonlinear Schrödinger equation SIAM Appl. Math. 61 1680-705 (Pubitemid 33099619)
-
(2001)
SIAM Journal on Applied Mathematics
, vol.61
, Issue.5
, pp. 1680-1705
-
-
Fibich, G.1
-
29
-
-
18144387631
-
Linear versus nonlinear dissipation for critical NLS equation
-
DOI 10.1016/j.physd.2005.03.011, PII S0167278905001181
-
Passot T, Sulem C and Sulem P L 2005 Linear versus nonlinear dissipation for critical NLS equation Physica D 203 167-84 (Pubitemid 40612257)
-
(2005)
Physica D: Nonlinear Phenomena
, vol.203
, Issue.3-4
, pp. 167-184
-
-
Passot, T.1
Sulem, C.2
Sulem, P.L.3
-
30
-
-
78049525386
-
Global well-posedness for cubic NLS with nonlinear damping
-
Antonelli P and Sparber C 2010 Global well-posedness for cubic NLS with nonlinear damping Commun. PDE 35 2310-28
-
(2010)
Commun. PDE
, vol.35
, pp. 2310-2328
-
-
Antonelli, P.1
Sparber, C.2
|