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Volumn 60, Issue 1, 1999, Pages 183-240

Self-focusing in the perturbed and unperturbed nonlinear Schrodinger equation in critical dimension

Author keywords

[No Author keywords available]

Indexed keywords

FOCUSING; NONLINEAR EQUATIONS; OPTICAL FIBERS; OPTICAL INSTRUMENT LENSES; PERTURBATION TECHNIQUES; RELAXATION PROCESSES; SENSITIVITY ANALYSIS;

EID: 0342647291     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139997322407     Document Type: Article
Times cited : (263)

References (82)
  • 1
    • 0018480221 scopus 로고
    • On the evolution of packets of water waves
    • M. ABLOWITZ AND H. SEGUR, On the evolution of packets of water waves, J. Fluid Mech., 92 (1979), pp. 691-715.
    • (1979) J. Fluid Mech. , vol.92 , pp. 691-715
    • Ablowitz, M.1    Segur, H.2
  • 3
    • 11944275339 scopus 로고
    • All-optical-switching and pulse amplification and steering in nonlinear fiber arrays
    • A. ACEVES, C. DE ANGELIS, G. LUTHER, A. RUBENCHIK, AND S. K. TURITSYN, All-optical-switching and pulse amplification and steering in nonlinear fiber arrays, Phys. Rev. Lett., 75 (1995), pp. 73-76.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 73-76
    • Aceves, A.1    De Angelis, C.2    Luther, G.3    Rubenchik, A.4    Turitsyn, S.K.5
  • 5
    • 58149212609 scopus 로고
    • Energy localization in nonlinear fiber arrays: Collapse effect compressor
    • A. ACEVES, G. LUTHER, C. DE ANGELIS, A. RUBENCHIK, AND S. K. TURITSYN, Energy localization in nonlinear fiber arrays: Collapse effect compressor, Phys. D, 87 (1995), pp. 262-272.
    • (1995) Phys. D , vol.87 , pp. 262-272
    • Aceves, A.1    Luther, G.2    De Angelis, C.3    Rubenchik, A.4    Turitsyn, S.K.5
  • 7
    • 0001035750 scopus 로고
    • Self-focusing and self-trapping of intense light beams in a nonlinear medium
    • S. AKHMANOV, A. SUKHORUKOV, AND R. KHOKHLOV, Self-focusing and self-trapping of intense light beams in a nonlinear medium, J. Experiment. Theoret. Phys., 23 (1966), pp. 1025-1033.
    • (1966) J. Experiment. Theoret. Phys. , vol.23 , pp. 1025-1033
    • Akhmanov, S.1    Sukhorukov, A.2    Khokhlov, R.3
  • 8
    • 0000056622 scopus 로고
    • Generation of a train of three-dimensional optical solitons in a self-focusing medium
    • N. AKHMEDIEV AND J. SOTO-CRESPO, Generation of a train of three-dimensional optical solitons in a self-focusing medium, Phys. Rev. A. 47 (1993), pp. 1358-1364.
    • (1993) Phys. Rev. A. , vol.47 , pp. 1358-1364
    • Akhmediev, N.1    Soto-Crespo, J.2
  • 9
    • 0012148319 scopus 로고
    • Galerkin finite element methods for the nonlinear Schrödinger equation
    • E. Lipitakis, ed., World Scientific, River Edge, NJ
    • G. AKRIVIS, V. DOUGALIS, O. KARAKASHIAN, AND W. MCKINNEY, Galerkin finite element methods for the nonlinear Schrödinger equation, in Advances on Computer Mathematics and Its Applications, E. Lipitakis, ed., World Scientific, River Edge, NJ, 1993, pp. 85-106.
    • (1993) Advances on Computer Mathematics and Its Applications , pp. 85-106
    • Akrivis, G.1    Dougalis, V.2    Karakashian, O.3    McKinney, W.4
  • 10
    • 84975674528 scopus 로고
    • Nonlinear asymmetric pulse distortion in long optical fibers
    • D. ANDERSON AND M. LISAK, Nonlinear asymmetric pulse distortion in long optical fibers, Opt. Lett., 7 (1982), pp. 394-396.
    • (1982) Opt. Lett. , vol.7 , pp. 394-396
    • Anderson, D.1    Lisak, M.2
  • 12
    • 0010902753 scopus 로고    scopus 로고
    • Multisplitting and collapse of self-focusing anisotropic beams in normal/anomalous media
    • L. BERGÉ AND J. RASMUSSEN, Multisplitting and collapse of self-focusing anisotropic beams in normal/anomalous media, Phys. Plasmas, 3 (1996), pp. 824-843.
    • (1996) Phys. Plasmas , vol.3 , pp. 824-843
    • Bergé, L.1    Rasmussen, J.2
  • 13
    • 0038959645 scopus 로고    scopus 로고
    • Pulse splitting of self-focusing beams in normally dispersive media
    • L. BERGÉ AND J. RASMUSSEN, Pulse splitting of self-focusing beams in normally dispersive media, Phys. Rev. A, 53 (1996), pp. 4476-4480.
    • (1996) Phys. Rev. A , vol.53 , pp. 4476-4480
    • Bergé, L.1    Rasmussen, J.2
  • 16
    • 0003197180 scopus 로고
    • An Introduction to Nonlinear Schrödinger Equation
    • UFRJ, Rio de Janeiro
    • T. CAZENAVE, An Introduction to Nonlinear Schrödinger Equation, Textos de metodos matematicos 22, UFRJ, Rio de Janeiro, 1989.
    • (1989) Textos de Metodos Matematicos , vol.22
    • Cazenave, T.1
  • 18
    • 84975557423 scopus 로고
    • Self-focusing of light pulses in the presence of normal group-velocity dispersion
    • P. CHERNEV AND V. PETROV, Self-focusing of light pulses in the presence of normal group-velocity dispersion, Opt. Lett., 17 (1992), pp. 172-174.
    • (1992) Opt. Lett. , vol.17 , pp. 172-174
    • Chernev, P.1    Petrov, V.2
  • 19
    • 84902428471 scopus 로고
    • Vector theory of self-focusing of an optical beam in Kerr media
    • S. CHI AND Q. GUO, Vector theory of self-focusing of an optical beam in Kerr media, Opt. Lett., 20 (1995), pp. 1598-1560.
    • (1995) Opt. Lett. , vol.20 , pp. 1598-11560
    • Chi, S.1    Guo, Q.2
  • 20
    • 36049053022 scopus 로고
    • Computer studies in self-focusing
    • E. DAWES AND J. MARBURGER, Computer studies in self-focusing, Phys. Rev., 179 (1969), pp. 862-868.
    • (1969) Phys. Rev. , vol.179 , pp. 862-868
    • Dawes, E.1    Marburger, J.2
  • 21
    • 44049117330 scopus 로고
    • Weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation
    • S. DYACHENKO, A. NEWELL, A. PUSHKAREV, AND V. ZAKHAROV, Optical turbulence: Weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation, Phys. D, 57 (1992), pp. 96-160.
    • (1992) Phys D , vol.57 , pp. 96-160
    • Dyachenko, S.1    Newell, A.2    Pushkarev, A.3    Zakharov, V.4    Turbulence, O.5
  • 22
    • 84975565826 scopus 로고
    • Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams
    • M. FEIT AND J. FLECK, Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams, J. Opt. Soc. Amer. B, 5 (1988), pp. 633-640.
    • (1988) J. Opt. Soc. Amer. B , vol.5 , pp. 633-640
    • Feit, M.1    Fleck, J.2
  • 24
    • 0000567112 scopus 로고    scopus 로고
    • An adiabatic law for self-focusing of optical beams
    • G. FIBICH, An adiabatic law for self-focusing of optical beams, Opt. Lett., 21 (1996), pp. 1735-1737.
    • (1996) Opt. Lett. , vol.21 , pp. 1735-1737
    • Fibich, G.1
  • 25
    • 0030567602 scopus 로고    scopus 로고
    • Small beam nonparaxiality arrests self-focusing of optical beams
    • G. FIBICH, Small beam nonparaxiality arrests self-focusing of optical beams, Phys. Rev. Lett., 76 (1996), pp. 4356-4359.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 4356-4359
    • Fibich, G.1
  • 26
    • 0038938431 scopus 로고
    • Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equation
    • G. FIBICH AND D. LEVY, Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equation, Phys. Lett. A, 249 (1988), pp. 286-294.
    • (1988) Phys. Lett. A , vol.249 , pp. 286-294
    • Fibich, G.1    Levy, D.2
  • 27
    • 0000389921 scopus 로고
    • Beam self-focusing in the presence of small normal time dispersion
    • G. FIBICH, V. MALKIN, AND G. PAPANICOLAOU, Beam self-focusing in the presence of small normal time dispersion, Phys. Rev. A. 52 (1995), pp. 4218-4228.
    • (1995) Phys. Rev. A. , vol.52 , pp. 4218-4228
    • Fibich, G.1    Malkin, V.2    Papanicolaou, G.3
  • 28
    • 0000566793 scopus 로고    scopus 로고
    • Self-focusing in the presence of small time dispersion and nonparaxiality
    • G. FIBICH AND G. PAPANICOLAOU, Self-focusing in the presence of small time dispersion and nonparaxiality, Opt. Lett., 22 (1997), pp. 1379-1381.
    • (1997) Opt. Lett. , vol.22 , pp. 1379-1381
    • Fibich, G.1    Papanicolaou, G.2
  • 29
    • 0000548165 scopus 로고
    • Asymptotic stability of manifold of self-similar solutions in self-focusing
    • G. FRAIMAN, Asymptotic stability of manifold of self-similar solutions in self-focusing, Sov. Phys. JETP, 61 (1985), pp. 228-233.
    • (1985) Sov. Phys. JETP , vol.61 , pp. 228-233
    • Fraiman, G.1
  • 30
    • 49249148441 scopus 로고
    • On a class of nonlinear Schrödinger equations. I: The Cauchy problem, general case
    • J. GINIBRE AND G. VELO, On a class of nonlinear Schrödinger equations. I: The Cauchy problem, general case, J. Funct. Anal., 32 (1979), pp. 1-32.
    • (1979) J. Funct. Anal. , vol.32 , pp. 1-32
    • Ginibre, J.1    Velo, G.2
  • 31
    • 0001404168 scopus 로고
    • On nonlinear Schrödinger equations
    • T. KATO, On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré. Phys. Théor, 46 (1987), pp. 113-129.
    • (1987) Ann. Inst. H. Poincaré. Phys. Théor , vol.46 , pp. 113-129
    • Kato, T.1
  • 32
    • 0000127687 scopus 로고
    • Self-focusing of optical beams
    • P. KELLEY, Self-focusing of optical beams, Phys. Rev. Lett., 15 (1965), pp. 1005-1008.
    • (1965) Phys. Rev. Lett. , vol.15 , pp. 1005-1008
    • Kelley, P.1
  • 33
    • 0013446331 scopus 로고
    • Nonlinearity and localization in one dimensional random media
    • A. R. Bishop, D. K. Campbell, and S. Pnevmaticos, eds., Springer Proceedings in Physics, Springer-Verlag. New York
    • R. KNAPP, G. C. PAPANICOLAOU, AND B. WHITE, Nonlinearity and localization in one dimensional random media, in Disorder and Nonlinearity, vol. 39, A. R. Bishop, D. K. Campbell, and S. Pnevmaticos, eds., Springer Proceedings in Physics, Springer-Verlag. New York, 1989, pp. 2-26.
    • (1989) Disorder and Nonlinearity , vol.39 , pp. 2-26
    • Knapp, R.1    Papanicolaou, G.C.2    White, B.3
  • 34
    • 0029394002 scopus 로고
    • Spatial structure of the focusing singularity of the nonlinear Schrödinger equation: A geometrical analysis
    • N. KOPPEL AND M. LANDMAN, Spatial structure of the focusing singularity of the nonlinear Schrödinger equation: A geometrical analysis. SIAM J. Appl. Math., 55 (1995), pp. 1297-1323.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 1297-1323
    • Koppel, N.1    Landman, M.2
  • 35
    • 44949272407 scopus 로고
    • Computer simulation of wave collapses in the nonlinear Schrödinger equation
    • N. KOSMATOV, V. SHVETS, AND V. ZAKHAROV, Computer simulation of wave collapses in the nonlinear Schrödinger equation, Phys. D, 52 (1991), pp. 16-35.
    • (1991) Phys. D , vol.52 , pp. 16-35
    • Kosmatov, N.1    Shvets, V.2    Zakharov, V.3
  • 37
    • 0000679239 scopus 로고
    • Analytic criterion for soliton instability in a nonlinear fiber array
    • E. LAEDKE, H. SPATSCHEK, AND S. TURITSYN, Analytic criterion for soliton instability in a nonlinear fiber array, Phys. Rev. E, 52 (1995), pp. 5549-5554.
    • (1995) Phys. Rev. E , vol.52 , pp. 5549-5554
    • Laedke, E.1    Spatschek, H.2    Turitsyn, S.3
  • 39
    • 0000893351 scopus 로고
    • Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
    • M. LANDMAN, G. PAPANICOLAOU, C. SULEM, AND P. SULEM, Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension, Phys. Rev. A, 38 (1988), pp. 3837-3843.
    • (1988) Phys. Rev. A , vol.38 , pp. 3837-3843
    • Landman, M.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.4
  • 40
    • 0006645185 scopus 로고
    • Stability of isotropic singularities for the nonlinear Schrödinger equation
    • M. LANDMAN, G. PAPANICOLAOU, C. SULEM, P. SULEM, AND X. WANG, Stability of isotropic singularities for the nonlinear Schrödinger equation, Phys. D, 47 (1991), pp. 393-415.
    • (1991) Phys. D , vol.47 , pp. 393-415
    • Landman, M.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.4    Wang, X.5
  • 41
    • 0002310685 scopus 로고
    • The focusing singularity of the nonlinear Schrödinger equation
    • M. Grandall, P. Rabinovitz, and R. Turner, ed., Academic Press, New York
    • B. LEMESURIER, G. PAPANICOLAOU, C. SULEM, AND P. SULEM, The focusing singularity of the nonlinear Schrödinger equation, in Directions in Partial Differential Equations, M. Grandall, P. Rabinovitz, and R. Turner, ed., Academic Press, New York, 1987, pp. 159-201.
    • (1987) Directions in Partial Differential Equations , pp. 159-201
    • Lemesurier, B.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.4
  • 42
    • 45549111243 scopus 로고
    • Focusing and multi-focusing solutions of the nonlinear Schrödinger equation
    • B. LEMESURIER, G. PAPANICOLAOU, C. SULEM, AND P. SULEM, Focusing and multi-focusing solutions of the nonlinear Schrödinger equation, Phys. D, 31 (1988), pp. 78-102.
    • (1988) Phys. D , vol.31 , pp. 78-102
    • Lemesurier, B.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.4
  • 43
    • 0001678668 scopus 로고
    • Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
    • B. LEMESURIER, G. PAPANICOLAOU, C. SULEM, AND P. SULEM, Local structure of the self-focusing singularity of the nonlinear Schrödinger equation, Phys. D, 32 (1988), pp. 210-226.
    • (1988) Phys. D , vol.32 , pp. 210-226
    • Lemesurier, B.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.4
  • 44
    • 43949157921 scopus 로고
    • The effects of normal dispersion on collapse events
    • G. LUTHER, A. NEWELL, AND J. MOLONEY, The effects of normal dispersion on collapse events. Phys. D, 74 (1994), pp. 59-73.
    • (1994) Phys. D , vol.74 , pp. 59-73
    • Luther, G.1    Newell, A.2    Moloney, J.3
  • 46
    • 0007375096 scopus 로고
    • Dynamics of wave, collapse in the critical case
    • V. MALKIN, Dynamics of wave, collapse in the critical case, Phys. Lett. A, 151 (1990), pp. 285-288.
    • (1990) Phys. Lett. A , vol.151 , pp. 285-288
    • Malkin, V.1
  • 47
    • 0001145199 scopus 로고
    • On the analytical theory for stationary self-focusinq of radiation
    • V. MALKIN, On the analytical theory for stationary self-focusinq of radiation, Phys. D, 64 (1993), pp. 251-266.
    • (1993) Phys. D , vol.64 , pp. 251-266
    • Malkin, V.1
  • 48
    • 2442572073 scopus 로고
    • Self-focusing: Theory
    • J. MARBURGER, Self-focusing: Theory, Prog. Quant. Electr., 4 (1975), pp. 35-110.
    • (1975) Prog. Quant. Electr. , vol.4 , pp. 35-110
    • Marburger, J.1
  • 49
    • 0041195908 scopus 로고
    • A stochastic Gaussian beam II
    • D. MCLAUGHLIN, A stochastic Gaussian beam II, J. Math Phys., 16 (1975), pp. 100-103.
    • (1975) J. Math Phys. , vol.16 , pp. 100-103
    • McLaughlin, D.1
  • 50
    • 35949022121 scopus 로고
    • Focusing singularity of the cubic Schrödinger equation
    • D. MCLAUGHLIN, G. PAPANICOLAOU, C. SULEM, AND P. SULEM, Focusing singularity of the cubic Schrödinger equation, Phys. Rev. A, 34 (1986), pp. 1200-1210.
    • (1986) Phys. Rev. A , vol.34 , pp. 1200-1210
    • McLaughlin, D.1    Papanicolaou, G.2    Sulem, C.3    Sulem, P.4
  • 51
    • 0001337201 scopus 로고
    • Construction of solutions with exactly k blow-up points for the Schrödinger equation with the critical power nonlinearity
    • F. MERLE, Construction of solutions with exactly k blow-up points for the Schrödinger equation with the critical power nonlinearity, Comm. Math. Phys., 129 (1990), pp. 223-240.
    • (1990) Comm. Math. Phys. , vol.129 , pp. 223-240
    • Merle, F.1
  • 52
    • 0030510597 scopus 로고    scopus 로고
    • Lower bounds for the blow-up rate of solutions of the Zakharov equation in dimension two
    • F. MERLE, Lower bounds for the blow-up rate of solutions of the Zakharov equation in dimension two, Comm. Pure Appl. Math., 49 (1996), pp. 765-794.
    • (1996) Comm. Pure Appl. Math. , vol.49 , pp. 765-794
    • Merle, F.1
  • 53
    • 0000704928 scopus 로고
    • 2 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. Differential Equations, 84 (1990), pp. 205-214.
    • (1990) J. Differential Equations , vol.84 , pp. 205-214
    • Merle, F.1    Tsutsumi, Y.2
  • 55
    • 84972577314 scopus 로고
    • Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity
    • H. NAWA, Asymptotic profiles of blow-up solutions of the nonlinear Schrödinger equation with critical power nonlinearity, J. Math. Soc. Japan, 46 (1994), pp. 557-586.
    • (1994) J. Math. Soc. Japan , vol.46 , pp. 557-586
    • Nawa, H.1
  • 56
    • 0000002410 scopus 로고
    • The focusing singularity of the Davey-Stewartson equations for gravity-capillary surface waves
    • G. PAPANICOLAOU, C. SULEM, P. SULEM, AND X. WANG, The focusing singularity of the Davey-Stewartson equations for gravity-capillary surface waves, Phys. D, 72 (1994), pp. 61-86.
    • (1994) Phys. D , vol.72 , pp. 61-86
    • Papanicolaou, G.1    Sulem, C.2    Sulem, P.3    Wang, X.4
  • 58
    • 0000664476 scopus 로고    scopus 로고
    • Radiative effects to the adiabatic dynamics of envelope-wave solitons
    • D. PELINOVSKY, Radiative effects to the adiabatic dynamics of envelope-wave solitons, Phys. D, 119 (1998), pp. 301-313.
    • (1998) Phys. D , vol.119 , pp. 301-313
    • Pelinovsky, D.1
  • 59
    • 84975660028 scopus 로고
    • Beam collapse as an explanation for anomalous ocular damage
    • J. POWELL, J. MOLONEY, A. NEWELL, AND R. ALBANESE, Beam collapse as an explanation for anomalous ocular damage, J. Opt. Soc. Amer. B, 10 (1993), pp. 1230-1241.
    • (1993) J. Opt. Soc. Amer. B , vol.10 , pp. 1230-1241
    • Powell, J.1    Moloney, J.2    Newell, A.3    Albanese, R.4
  • 60
    • 6144262089 scopus 로고    scopus 로고
    • Observation of pulse splitting in nonlinear dispersive media
    • J. RANKA, R. SCHIRMER, AND A. GAETA, Observation of pulse splitting in nonlinear dispersive media, Phys. Rev. Lett., 77 (1996), pp. 3783-3786.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 3783-3786
    • Ranka, J.1    Schirmer, R.2    Gaeta, A.3
  • 61
    • 84956263763 scopus 로고
    • Blow-up in nonlinear Schrödinger equations-I a general review
    • J. RASMUSSEN AND K. RYPDAL, Blow-up in nonlinear Schrödinger equations-I a general review, Phys. Scripta, 33 (1986), pp. 481-497.
    • (1986) Phys. Scripta , vol.33 , pp. 481-497
    • Rasmussen, J.1    Rypdal, K.2
  • 62
    • 84956239507 scopus 로고
    • Blow-up in nonlinear Schrödinger equations-II similarity structure of the blow-up singularity
    • J. RASMUSSEN AND K. RYPDAL, Blow-up in nonlinear Schrödinger equations-II similarity structure of the blow-up singularity, Phys. Scripta, 33 (1986), pp. 498-504.
    • (1986) Phys. Scripta , vol.33 , pp. 498-504
    • Rasmussen, J.1    Rypdal, K.2
  • 63
    • 85037955325 scopus 로고
    • Princeton Plasma Physics Laboratory Princeton, NJ
    • B. ROCKWELL, Princeton Plasma Physics Laboratory, Princeton, NJ, 1991.
    • (1991)
    • Rockwell, B.1
  • 64
    • 84975568044 scopus 로고
    • Pulse splitting during self-focusing in normally dispersive media
    • J. ROTHENBERG, Pulse splitting during self-focusing in normally dispersive media, Opt. Lett., 17 (1992), pp. 583-585.
    • (1992) Opt. Lett. , vol.17 , pp. 583-585
    • Rothenberg, J.1
  • 65
    • 20444430721 scopus 로고
    • Space-time focusing: Breakdown of the slowly varying envelope approximation in the self-focusing of femtosecond pulses
    • J. ROTHENBERG, Space-time focusing: Breakdown of the slowly varying envelope approximation in the self-focusing of femtosecond pulses, Opt. Lett., 17 (1992), pp. 1340-1342.
    • (1992) Opt. Lett. , vol.17 , pp. 1340-1342
    • Rothenberg, J.1
  • 66
    • 3943090568 scopus 로고
    • Self-focusing: Experimental
    • Y. SHEN, Self-focusing: Experimental, Prog. Quant. Electr., 4 (1975), pp. 1-34.
    • (1975) Prog. Quant. Electr. , vol.4 , pp. 1-34
    • Shen, Y.1
  • 67
    • 0342705527 scopus 로고
    • Numerical calculations of self-focusing and trapping of a short light pulse, in Kerr liquids
    • F. SHIMIZU, Numerical calculations of self-focusing and trapping of a short light pulse, in Kerr liquids, IBM J. Res. Dev., 17 (1973), pp. 286-298.
    • (1973) IBM J. Res. Dev. , vol.17 , pp. 286-298
    • Shimizu, F.1
  • 68
    • 0027642521 scopus 로고
    • Description of the self-focusing and collapse effects by a modified nonlinear Schrödinger equation
    • J. SOTO-CRESPO AND N. AKHMEDIEV, Description of the self-focusing and collapse effects by a modified nonlinear Schrödinger equation, Optics Comm., 101 (1993), pp. 223-230.
    • (1993) Optics Comm. , vol.101 , pp. 223-230
    • Soto-Crespo, J.1    Akhmediev, N.2
  • 70
    • 0007434482 scopus 로고    scopus 로고
    • Focusing nonlinear Schrödinger equation and wave-packet collapse
    • C. SULEM AND P. SULEM, Focusing nonlinear Schrödinger equation and wave-packet collapse, Nonlinear Anal. Theor., 30 (1997), pp. 833-844.
    • (1997) Nonlinear Anal. Theor. , vol.30 , pp. 833-844
    • Sulem, C.1    Sulem, P.2
  • 72
    • 0040580243 scopus 로고
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power
    • 2 concentration of blow-up solutions for the nonlinear Schrödinger equation with critical power, Nonlinear Anal., 15 (1990), pp. 719-724.
    • (1990) Nonlinear Anal. , vol.15 , pp. 719-724
    • Tsutsumi, Y.1
  • 73
    • 0002631531 scopus 로고
    • Nonstable solitons and sharp criteria for wave collapse
    • S. TURITSYN, Nonstable solitons and sharp criteria for wave collapse, Phys. Rev. E, 47 (1993), pp. R13-R16.
    • (1993) Phys. Rev. E , vol.47
    • Turitsyn, S.1
  • 74
    • 6144227165 scopus 로고    scopus 로고
    • Electromagnetic beam breakup - Multiple filaments, single beam equilibria and radiation
    • F. VIDAL AND T. JOHNSTON, Electromagnetic beam breakup - multiple filaments, single beam equilibria and radiation, Phys. Rev. Lett., 77 (1996), pp. 1282-1285.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 1282-1285
    • Vidal, F.1    Johnston, T.2
  • 75
    • 0000707128 scopus 로고
    • Averaged description of wave beams in linear and nonlinear media
    • in Russian
    • S. VLASOV, V. PETRISHCHEV, AND V. TALANOV, Averaged description of wave beams in linear and nonlinear media, Izv. Vuz Radiofiz, 14 (1971), pp. 1353-1363 (in Russian); Radiophys. and Quantum Electronics, 14 (1971), pp. 1062-1070 (in English).
    • (1971) Izv. Vuz Radiofiz , vol.14 , pp. 1353-1363
    • Vlasov, S.1    Petrishchev, V.2    Talanov, V.3
  • 76
    • 18644384025 scopus 로고
    • in English
    • S. VLASOV, V. PETRISHCHEV, AND V. TALANOV, Averaged description of wave beams in linear and nonlinear media, Izv. Vuz Radiofiz, 14 (1971), pp. 1353-1363 (in Russian); Radiophys. and Quantum Electronics, 14 (1971), pp. 1062-1070 (in English).
    • (1971) Radiophys. and Quantum Electronics , vol.14 , pp. 1062-1070
  • 77
    • 0041473959 scopus 로고
    • Nonlinear Schrödinger equations and sharp interpolation estimates
    • M. WEINSTEIN, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys., 87 (1983), pp. 567-576.
    • (1983) Comm. Math. Phys. , vol.87 , pp. 567-576
    • Weinstein, M.1
  • 78
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • M. WEINSTEIN, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal., 16 (1985), pp. 472-491.
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 472-491
    • Weinstein, M.1
  • 79
    • 0009156882 scopus 로고
    • The Nonlinear Schrödinger Equations - Singularity Formation, Stability and Dispersion
    • AMS, Providence, RI
    • M. WEINSTEIN, The Nonlinear Schrödinger Equations - Singularity Formation, Stability and Dispersion, Contemp. Math. 99, AMS, Providence, RI, 1989, pp. 213-232.
    • (1989) Contemp. Math. , vol.99 , pp. 213-232
    • Weinstein, M.1
  • 80
    • 0141745603 scopus 로고    scopus 로고
    • Excitation and dynamics of pulses in coupled fiber arrays
    • M. WEINSTEIN AND B. YEARY, Excitation and dynamics of pulses in coupled fiber arrays, Phys. Lett. A, 222 (1996), pp. 157-162.
    • (1996) Phys. Lett. A , vol.222 , pp. 157-162
    • Weinstein, M.1    Yeary, B.2
  • 81
    • 0003908012 scopus 로고
    • Optical Waves in Crystals: Propagation and Control of Laser Radiation
    • Wiley, New York
    • A. YARIV, Optical Waves in Crystals: Propagation and Control of Laser Radiation, Wiley Ser. Pure Appl. Optics, Wiley, New York, 1984.
    • (1984) Wiley Ser. Pure Appl. Optics
    • Yariv, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.