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Volumn 155, Issue 1-2, 2001, Pages 132-158

Self-focusing on bounded domains

Author keywords

Blowup; Collapse; Critical power; Hollow fiber; Nonlinear Schr dinger equation; Singularity formation; Stability; Waveguide

Indexed keywords


EID: 0035400338     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00249-4     Document Type: Article
Times cited : (55)

References (32)
  • 1
    • 85120120991 scopus 로고    scopus 로고
    • H. Berestycki, T. Gallouët, O. Kavian, Equations de champs scalaires euclidiens nonlinéaires dans le plan (French) [Nonlinear euclidean scalar field equations in the plane], C.R. Acad. Sci. Paris 297, Série I (1983) 307–310.
  • 2
    • 0020591566 scopus 로고
    • Nonlinear scalar field equations II. Existence of infinitely many solutions
    • H. Berestycki P.L. Lions Nonlinear scalar field equations II. Existence of infinitely many solutions Arch. Rational Mech. Anal. 82 1983 347 375
    • (1983) Arch. Rational Mech. Anal. , vol.82 , pp. 347-375
    • Berestycki, H.1    Lions, P.L.2
  • 3
    • 85120099098 scopus 로고    scopus 로고
    • J. Bourgain, Construction of quasi-periodic solutions for Hamiltonian perturbations of linear equations and applications to nonlinear PDE, Internat. Math. Res. Notices, 1994, 475 ff., approx. 21 pp. (Electronic).
  • 4
    • 49149142420 scopus 로고
    • Nonlinear Schrödinger evolution equations
    • H. Brezis T. Gallouet Nonlinear Schrödinger evolution equations Nonlinear Anal. 4 1980 677 681
    • (1980) Nonlinear Anal. , vol.4 , pp. 677-681
    • Brezis, H.1    Gallouet, T.2
  • 5
    • 85120117247 scopus 로고    scopus 로고
    • G. Fibich, Self-focusing in the damped nonlinear Schrödinger equation, SIAM J. Appl. Math. 61 (2001) 1680–1705.
  • 6
    • 0001576369 scopus 로고    scopus 로고
    • Critical power for self-focusing in bulk media and in hollow waveguides
    • G. Fibich A. Gaeta Critical power for self-focusing in bulk media and in hollow waveguides Opt. Lett. 25 2000 335 337
    • (2000) Opt. Lett. , vol.25 , pp. 335-337
    • Fibich, G.1    Gaeta, A.2
  • 7
    • 0034355739 scopus 로고    scopus 로고
    • Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation
    • G. Fibich B. Ilan Self-focusing of elliptic beams: an example of the failure of the aberrationless approximation JOSA B 17 2000 1749 1758
    • (2000) JOSA B , vol.17 , pp. 1749-1758
    • Fibich, G.1    Ilan, B.2
  • 8
    • 0342647291 scopus 로고    scopus 로고
    • Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension
    • G. Fibich G.C. Papanicolaou Self-focusing in the perturbed and unperturbed nonlinear Schrödinger equation in critical dimension SIAM J. Appl. Math. 60 1999 183 240
    • (1999) SIAM J. Appl. Math. , vol.60 , pp. 183-240
    • Fibich, G.1    Papanicolaou, G.C.2
  • 9
    • 34250271532 scopus 로고
    • Symmetry and related properties via the maximum principle
    • B. Gidas W.M. Ni L. Nirenburg Symmetry and related properties via the maximum principle Commun. Math. Phys. 68 1979 209 243
    • (1979) Commun. Math. Phys. , vol.68 , pp. 209-243
    • Gidas, B.1    Ni, W.M.2    Nirenburg, L.3
  • 11
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger equations I. The Cauchy problem, general case
    • J. Ginibre G. Velo On a class of nonlinear Schrödinger equations I. The Cauchy problem, general case J. Funct. Anal. 32 1979 1 32
    • (1979) J. Funct. Anal. , vol.32 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 12
    • 38249018099 scopus 로고
    • Existence of nodal solutions of semilinear equations in rN
    • N J. Diff. Eqs. 85 2 1990 367 400
    • (1990) J. Diff. Eqs. , vol.85 , Issue.2 , pp. 367-400
    • Grillakis, M.1
  • 13
    • 0001464965 scopus 로고    scopus 로고
    • Nonlinear propagation dynamics of an ultrashort pulse in a hollow waveguide
    • D. Homoelle A.L. Gaeta Nonlinear propagation dynamics of an ultrashort pulse in a hollow waveguide Opt. Lett. 25 2000 761 763
    • (2000) Opt. Lett. , vol.25 , pp. 761-763
    • Homoelle, D.1    Gaeta, A.L.2
  • 14
    • 0001325292 scopus 로고
    • A remark on the blowing-up of solutions to the Cauchy problem for nonlinear Schrödinger equations
    • O. Kavian A remark on the blowing-up of solutions to the Cauchy problem for nonlinear Schrödinger equations Trans. Am. Math. Soc. 299 1987 193 203
    • (1987) Trans. Am. Math. Soc. , vol.299 , pp. 193-203
    • Kavian, O.1
  • 16
    • 84893892336 scopus 로고
    • Hollow metallic and dielectric waveguides for long distance optical transmission and lasers
    • E.A.J. Marcatili R.A. Schmeltzer Hollow metallic and dielectric waveguides for long distance optical transmission and lasers Bell Syst. Tech. J. 43 1964 1783 1809
    • (1964) Bell Syst. Tech. J. , vol.43 , pp. 1783-1809
    • Marcatili, E.A.J.1    Schmeltzer, R.A.2
  • 17
    • 84990553632 scopus 로고
    • On uniqueness and continuation properties after blow-up time of self-similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass
    • F. Merle 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 1992 203 254
    • (1992) Commun. Pure Appl. Math. , vol.45 , pp. 203-254
    • Merle, F.1
  • 18
    • 84974001368 scopus 로고
    • Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power
    • F. Merle Determination of blow-up solutions with minimal mass for nonlinear Schrödinger equation with critical power Duke Math. J. 69 1993 427 454
    • (1993) Duke Math. J. , vol.69 , pp. 427-454
    • Merle, F.1
  • 19
    • 85120103510 scopus 로고    scopus 로고
    • F. Merle, Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations, in: Proceedings of the International Congress of Mathematicians, Vol. 3, 1998, pp. 57–66.
  • 20
    • 0000704928 scopus 로고
    • L2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power nonlinearity J. Diff. Eqs. 84 1990 205 214
    • (1990) J. Diff. Eqs. , vol.84 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 21
    • 0000240026 scopus 로고    scopus 로고
    • Optical pulse compression: bulk media versus hollow waveguides
    • N. Milosevic G.Tempea T. Brabec Optical pulse compression: bulk media versus hollow waveguides Opt. Lett. 25 2000 672 674
    • (2000) Opt. Lett. , vol.25 , pp. 672-674
    • Milosevic, N.1    G.Tempea2    Brabec, T.3
  • 22
    • 0030141567 scopus 로고    scopus 로고
    • Generation of high energy 10 fs pulses by a new pulse compression technique
    • M. Nisoli S. De Silvestri O. Svelto Generation of high energy 10 fs pulses by a new pulse compression technique Appl. Phys. Lett. 68 1996 1795 2793
    • (1996) Appl. Phys. Lett. , vol.68 , pp. 1795-2793
    • Nisoli, M.1    De Silvestri, S.2    Svelto, O.3
  • 25
    • 85120122095 scopus 로고    scopus 로고
    • G. Polya, G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, NJ, 1951.
  • 26
    • 0000173206 scopus 로고
    • On the bound states of the nonlinear Schrödinger equation with a linear potential
    • H.A. Rose M.I. Weinstein On the bound states of the nonlinear Schrödinger equation with a linear potential Physica D 30 1988 207 218
    • (1988) Physica D , vol.30 , pp. 207-218
    • Rose, H.A.1    Weinstein, M.I.2
  • 27
    • 0001420204 scopus 로고
    • Instability of nonlinear bound states
    • J. Shatah W.A. Strauss Instability of nonlinear bound states Commun. Math. Phys. 100 1985 173 190
    • (1985) Commun. Math. Phys. , vol.100 , pp. 173-190
    • Shatah, J.1    Strauss, W.A.2
  • 28
    • 85120109953 scopus 로고    scopus 로고
    • C. Sulem, P.L. Sulem, The Nonlinear Schrödinger Equation, Springer, New York, 1999.
  • 29
    • 0442272981 scopus 로고    scopus 로고
    • Nonlinear source for the generation of high-energy few-cycle optical pulses
    • G. Tempea T. Brabec Nonlinear source for the generation of high-energy few-cycle optical pulses Opt. Lett. 23 1998 1286 1288
    • (1998) Opt. Lett. , vol.23 , pp. 1286-1288
    • Tempea, G.1    Brabec, T.2
  • 30
    • 0000846277 scopus 로고    scopus 로고
    • Theory of self-focusing in a hollow waveguide
    • G. Tempea T. Brabec Theory of self-focusing in a hollow waveguide Opt. Lett. 23 1998 762 764
    • (1998) Opt. Lett. , vol.23 , pp. 762-764
    • Tempea, G.1    Brabec, T.2
  • 31
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M.I. Weinstein Nonlinear Schrödinger equations and sharp interpolation estimates Commun. Math. Phys. 87 1983 567 576
    • (1983) Commun. Math. Phys. , vol.87 , pp. 567-576
    • Weinstein, M.I.1
  • 32
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • M.I. Weinstein Lyapunov stability of ground states of nonlinear dispersive evolution equations Commun. Pure Appl. Math. 39 1986 51 68
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 51-68
    • Weinstein, M.I.1


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