메뉴 건너뛰기




Volumn 152-153, Issue , 2001, Pages 269-287

Traveling hole solutions of the complex Ginzburg-Landau equation: A review

Author keywords

Complex Ginzburg Landau equation; Phase instability; Traveling hole solutions

Indexed keywords


EID: 0035873648     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00174-9     Document Type: Article
Times cited : (60)

References (66)
  • 2
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • Cross M.C., Hohenberg P.C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65:1993;851-1112.
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 3
    • 0000484304 scopus 로고
    • The time-dependent amplitude equation for the Swift-Hohenberg problem
    • Collet P., Eckmann J.-P. The time-dependent amplitude equation for the Swift-Hohenberg problem. Commun. Math. Phys. 132:1990;139-153.
    • (1990) Commun. Math. Phys. , vol.132 , pp. 139-153
    • Collet, P.1    Eckmann, J.-P.2
  • 4
    • 0343318679 scopus 로고
    • Amplitude analysis of the Swift-Hohenberg equation
    • P. Collet, Amplitude analysis of the Swift-Hohenberg equation, Eur. J. Mech. B 10 (Suppl. 2) (1991) 119-124.
    • (1991) Eur. J. Mech. B , vol.10 , Issue.SUPPL. 2 , pp. 119-124
    • Collet, P.1
  • 5
    • 0001545279 scopus 로고
    • On the validity of the Ginzburg-Landau equation
    • van Harten A. On the validity of the Ginzburg-Landau equation. J. Nonlinear Sci. 1:1991;397-422.
    • (1991) J. Nonlinear Sci. , vol.1 , pp. 397-422
    • Van Harten, A.1
  • 6
  • 7
    • 0001656215 scopus 로고
    • Error estimates for the Ginzburg-Landau approximation
    • Schneider G. Error estimates for the Ginzburg-Landau approximation. Z. Angew. Math. Phys. 45:1994;433-457.
    • (1994) Z. Angew. Math. Phys. , vol.45 , pp. 433-457
    • Schneider, G.1
  • 8
    • 21344476138 scopus 로고
    • Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations
    • Schneider G. Global existence via Ginzburg-Landau formalism and pseudo-orbits of Ginzburg-Landau approximations. Commun. Math. Phys. 164:1994;157-179.
    • (1994) Commun. Math. Phys. , vol.164 , pp. 157-179
    • Schneider, G.1
  • 10
    • 0000454926 scopus 로고
    • Attractors for modulation equations on unbounded domains - Existence and comparison
    • Mielke A., Schneider G. Attractors for modulation equations on unbounded domains - existence and comparison. Nonlinearity. 8:1995;743-768.
    • (1995) Nonlinearity , vol.8 , pp. 743-768
    • Mielke, A.1    Schneider, G.2
  • 14
    • 4243776283 scopus 로고    scopus 로고
    • Pattern Formation and Instabilities in Continuous Dissipative Systems
    • (Eds.)
    • H.R. Brand, H. Flaschka, A.C. Newell (Eds.), Pattern Formation and Instabilities in Continuous Dissipative Systems, Physica D 97 (1-3) (1996).
    • (1996) Physica D , vol.97 , Issue.1-3
    • Brand, H.R.1    Flaschka, H.2    Newell, A.C.3
  • 15
    • 0000882460 scopus 로고
    • Special issue on nonlinear optical structures, patterns, chaos
    • (Eds.)
    • L.A. Lugiato, M.S. El Naschie (Eds.), Special issue on nonlinear optical structures, patterns, chaos, Chaos, Solitons and Fractals 4 (8-9) (1994).
    • (1994) Chaos, Solitons and Fractals , vol.4 , Issue.8-9
    • Lugiato, L.A.1    El Naschie, M.S.2
  • 17
    • 0003001381 scopus 로고
    • Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation
    • Bekki N., Nozaki K. Formations of spatial patterns and holes in the generalized Ginzburg-Landau equation. Phys. Lett. A. 110:1985;133-135.
    • (1985) Phys. Lett. a , vol.110 , pp. 133-135
    • Bekki, N.1    Nozaki, K.2
  • 18
    • 0003351373 scopus 로고
    • Chemical Oscillations, Waves and Turbulence
    • Springer, Berlin
    • Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer Series in Synergetics, Vol. 19, Springer, Berlin, 1984.
    • (1984) Springer Series in Synergetics , vol.19
    • Kuramoto, Y.1
  • 21
    • 0004286934 scopus 로고
    • Springer, New York
    • H. Haken, Synergetics, Springer, New York, 1978.
    • (1978) Synergetics
    • Haken, H.1
  • 23
    • 0000507179 scopus 로고
    • Persistent propagation of concentration waves in dissipative media far from thermal equilibrium
    • Kuramoto Y., Tsuzuki T. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Prog. Theoret. Phys. 55:1976;356-369.
    • (1976) Prog. Theoret. Phys. , vol.55 , pp. 356-369
    • Kuramoto, Y.1    Tsuzuki, T.2
  • 24
    • 0017554878 scopus 로고
    • Nonlinear analysis of hydrodynamic instability in laminar flames. I. Derivation of basic equations
    • Sivashinsky G.I. Nonlinear analysis of hydrodynamic instability in laminar flames. I. Derivation of basic equations. Acta Astron. 4:1977;1177-1206.
    • (1977) Acta Astron. , vol.4 , pp. 1177-1206
    • Sivashinsky, G.I.1
  • 25
    • 0001471553 scopus 로고
    • Breakdown of the phase dynamics
    • Sakaguchi H. Breakdown of the phase dynamics. Prog. Theoret. Phys. 84:1990;792-800.
    • (1990) Prog. Theoret. Phys. , vol.84 , pp. 792-800
    • Sakaguchi, H.1
  • 26
    • 0018702717 scopus 로고
    • Stability and fluctuations of a spatially periodic convective flow
    • Pomeau Y., Manneville P. Stability and fluctuations of a spatially periodic convective flow. J. Phys. Lett. Paris. 40:1979;L609-L612.
    • (1979) J. Phys. Lett. Paris , vol.40
    • Pomeau, Y.1    Manneville, P.2
  • 28
    • 0024704294 scopus 로고
    • A form of turbulence associated with defects
    • Coullet P., Gil L., Lega J. A form of turbulence associated with defects. Physica D. 37:1989;91-103.
    • (1989) Physica D , vol.37 , pp. 91-103
    • Coullet, P.1    Gil, L.2    Lega, J.3
  • 29
    • 84956120762 scopus 로고
    • Defect-mediated turbulence in wave patterns
    • Coullet P., Lega J. Defect-mediated turbulence in wave patterns. Europhys. Lett. 7:1988;511-516.
    • (1988) Europhys. Lett. , vol.7 , pp. 511-516
    • Coullet, P.1    Lega, J.2
  • 30
    • 0001483038 scopus 로고
    • Traveling waves and defect-initiated turbulence in electroconvecting nematics
    • Rehberg I., Rasenat S., Steinberg V. Traveling waves and defect-initiated turbulence in electroconvecting nematics. Phys. Rev. Lett. 62:1989;756-759.
    • (1989) Phys. Rev. Lett. , vol.62 , pp. 756-759
    • Rehberg, I.1    Rasenat, S.2    Steinberg, V.3
  • 31
    • 4043097649 scopus 로고    scopus 로고
    • Phase diagram of the two-dimensional complex Ginzburg-Landau equation
    • Chaté H., Manneville P. Phase diagram of the two-dimensional complex Ginzburg-Landau equation. Physica A. 224:1996;348-368.
    • (1996) Physica a , vol.224 , pp. 348-368
    • Chaté, H.1    Manneville, P.2
  • 32
    • 0002853768 scopus 로고    scopus 로고
    • Phase turbulence in the two-dimensional complex Ginzburg-Landau equation
    • Manneville P., Chaté H. Phase turbulence in the two-dimensional complex Ginzburg-Landau equation. Physica D. 96:1996;30-46.
    • (1996) Physica D , vol.96 , pp. 30-46
    • Manneville, P.1    Chaté, H.2
  • 34
    • 0041195842 scopus 로고
    • Space and time intermittency behaviour of a one-dimensional Ginzburg-Landau equation
    • Gil L. Space and time intermittency behaviour of a one-dimensional Ginzburg-Landau equation. Nonlinearity. 4:1991;1213-1222.
    • (1991) Nonlinearity , vol.4 , pp. 1213-1222
    • Gil, L.1
  • 36
    • 33748335189 scopus 로고
    • Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation
    • Chaté H. Spatiotemporal intermittency regimes of the one-dimensional complex Ginzburg-Landau equation. Nonlinearity. 7:1994;185-204.
    • (1994) Nonlinearity , vol.7 , pp. 185-204
    • Chaté, H.1
  • 37
    • 0000558599 scopus 로고    scopus 로고
    • Building blocks of spatiotemporal intermittency
    • van Hecke M. Building blocks of spatiotemporal intermittency. Phys. Rev. Lett. 80:1998;1896-1899.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 1896-1899
    • Van Hecke, M.1
  • 38
    • 0035873577 scopus 로고    scopus 로고
    • Dispersive wave turbulence in one dimension
    • D. Cai, A.J. Majda, D.W. McLaughlin, E.G. Tabak, Dispersive wave turbulence in one dimension, Physica D 152-153 (2001) 551-572.
    • (2001) Physica D , vol.152-153 , pp. 551-572
    • Cai, D.1    Majda, A.J.2    McLaughlin, D.W.3    Tabak, E.G.4
  • 41
    • 0002961857 scopus 로고
    • Direct method of finding exact solutions of nonlinear evolution equations
    • in: R.M. Miura (Ed.) Springer, Berlin
    • R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in: R.M. Miura (Ed.), Bäcklund Transformations, Lecture Notes in Mathematics, Vol. 515, Springer, Berlin, 1976, pp. 40-68.
    • (1976) Bäcklund Transformations, Lecture Notes in Mathematics , vol.515 , pp. 40-68
    • Hirota, R.1
  • 42
    • 44049115047 scopus 로고
    • Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations
    • van Saarloos W., Hohenberg P.C. Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations. Physica D. 56:1992;303-367.
    • (1992) Physica D , vol.56 , pp. 303-367
    • Van Saarloos, W.1    Hohenberg, P.C.2
  • 43
    • 58149209842 scopus 로고
    • Hole solutions in the 1D complex Ginzburg-Landau equation
    • Popp S., Stiller O., Aranson I., Kramer L. Hole solutions in the 1D complex Ginzburg-Landau equation. Physica D. 84:1995;398-423.
    • (1995) Physica D , vol.84 , pp. 398-423
    • Popp, S.1    Stiller, O.2    Aranson, I.3    Kramer, L.4
  • 44
    • 22244440233 scopus 로고    scopus 로고
    • Breaking the hidden symmetry in the Ginzburg-Landau equation
    • Doelman A. Breaking the hidden symmetry in the Ginzburg-Landau equation. Physica D. 97:1996;398-428.
    • (1996) Physica D , vol.97 , pp. 398-428
    • Doelman, A.1
  • 45
    • 0000902465 scopus 로고    scopus 로고
    • Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons
    • Lega J., Fauve S. Traveling hole solutions to the complex Ginzburg-Landau equation as perturbations of nonlinear Schrödinger dark solitons. Physica D. 102:1997;234-252.
    • (1997) Physica D , vol.102 , pp. 234-252
    • Lega, J.1    Fauve, S.2
  • 46
    • 0000884205 scopus 로고
    • Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation
    • Popp S., Stiller O., Aranson I., Weber A., Kramer L. Localized hole solutions and spatiotemporal chaos in the 1D complex Ginzburg-Landau equation. Phys. Rev. Lett. 70:1993;3880-3883.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 3880-3883
    • Popp, S.1    Stiller, O.2    Aranson, I.3    Weber, A.4    Kramer, L.5
  • 47
    • 0000843673 scopus 로고
    • From dark solitons in the defocusing nonlinear Schrödinger equation to holes in the complex Ginzburg-Landau equation
    • Stiller O., Popp S., Kramer L. From dark solitons in the defocusing nonlinear Schrödinger equation to holes in the complex Ginzburg-Landau equation. Physica D. 84:1995;424-436.
    • (1995) Physica D , vol.84 , pp. 424-436
    • Stiller, O.1    Popp, S.2    Kramer, L.3
  • 49
    • 0001246139 scopus 로고
    • Model for the transition in bluff body wakes
    • Leweke T., Provensal M. Model for the transition in bluff body wakes. Phys. Rev. Lett. 72:1994;3174-3177.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 3174-3177
    • Leweke, T.1    Provensal, M.2
  • 50
  • 51
    • 0343676826 scopus 로고
    • Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion
    • Hasegawa A., Tappert F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion. Appl. Phys. Lett. 23:1973;142-144.
    • (1973) Appl. Phys. Lett. , vol.23 , pp. 142-144
    • Hasegawa, A.1    Tappert, F.2
  • 52
    • 84975576394 scopus 로고
    • Solitary pulses in an amplified nonlinear dispersive medium
    • Bélanger P.A., Gagnon L., Paré C. Solitary pulses in an amplified nonlinear dispersive medium. Opt. Lett. 14:1989;943-945.
    • (1989) Opt. Lett. , vol.14 , pp. 943-945
    • Bélanger, P.A.1    Gagnon, L.2    Paré, C.3
  • 53
    • 36849110613 scopus 로고
    • Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion
    • Hasegawa A., Tappert F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23:1973;171-172.
    • (1973) Appl. Phys. Lett. , vol.23 , pp. 171-172
    • Hasegawa, A.1    Tappert, F.2
  • 54
    • 0000169358 scopus 로고
    • Interaction between solitons in a stable medium
    • V.E. Zakharov, A.B. Shabat, Interaction between solitons in a stable medium, Sov. Phys. JETP 37 (1973) 823-828 [Zhurnal-Eksperimental'noi-i-Teoreticheskoi-Fiziki 64 (1973) 1627-1639].
    • (1973) Sov. Phys. JETP , vol.37 , pp. 823-828
    • Zakharov, V.E.1    Shabat, A.B.2
  • 55
    • 0001442403 scopus 로고
    • V.E. Zakharov, A.B. Shabat, Interaction between solitons in a stable medium, Sov. Phys. JETP 37 (1973) 823-828 [Zhurnal-Eksperimental'noi-i-Teoreticheskoi-Fiziki 64 (1973) 1627-1639].
    • (1973) Zhurnal-Eksperimental'noi-i-Teoreticheskoi-Fiziki , vol.64 , pp. 1627-1639
  • 56
    • 0030855569 scopus 로고    scopus 로고
    • Stabilization of dark-soliton transmission by means of nonlinear gain
    • Ikeda H., Matsumoto M., Hasegawa A. Stabilization of dark-soliton transmission by means of nonlinear gain. J. Opt. Soc. Am. B. 14:1997;136-143.
    • (1997) J. Opt. Soc. Am. B , vol.14 , pp. 136-143
    • Ikeda, H.1    Matsumoto, M.2    Hasegawa, A.3
  • 57
    • 0000711299 scopus 로고
    • Perturbation-induced dynamics of dark solitons
    • and references quoted therein
    • Y.S. Kivshar, Y. Xiaoping, Perturbation-induced dynamics of dark solitons, Phys. Rev. E 49 (1994) 1657-1670, and references quoted therein.
    • (1994) Phys. Rev. e , vol.49 , pp. 1657-1670
    • Kivshar, Y.S.1    Xiaoping, Y.2
  • 59
    • 0032122078 scopus 로고    scopus 로고
    • Effect of nonlinear gain on dark solitons
    • Chen X.-J., Chen Z.-D. Effect of nonlinear gain on dark solitons. IEEE J. Quant. Electron. 34:1998;1308-1311.
    • (1998) IEEE J. Quant. Electron. , vol.34 , pp. 1308-1311
    • Chen, X.-J.1    Chen, Z.-D.2
  • 60
    • 0031498009 scopus 로고    scopus 로고
    • Nonadiabatic dynamics of dark solitons
    • Burtsev S., Camassa R. Nonadiabatic dynamics of dark solitons. J. Opt. Soc. Am. B. 14:1997;1782-1787.
    • (1997) J. Opt. Soc. Am. B , vol.14 , pp. 1782-1787
    • Burtsev, S.1    Camassa, R.2
  • 62
    • 0033628312 scopus 로고    scopus 로고
    • Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
    • Kapitula T., Rubin J. Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Nonlinearity. 13:2000;77-112.
    • (2000) Nonlinearity , vol.13 , pp. 77-112
    • Kapitula, T.1    Rubin, J.2
  • 63
    • 36049053467 scopus 로고
    • Intrinsic resistive transition in narrow superconductive channels
    • Langer J.S., Ambegaokar V. Intrinsic resistive transition in narrow superconductive channels. Phys. Rev. 164:1967;498-510.
    • (1967) Phys. Rev. , vol.164 , pp. 498-510
    • Langer, J.S.1    Ambegaokar, V.2
  • 64
    • 0001558997 scopus 로고
    • Instability of the hole solution in the complex Ginzburg-Landau equation
    • Sakaguchi H. Instability of the hole solution in the complex Ginzburg-Landau equation. Prog. Theoret. Phys. 85:1991;417-421.
    • (1991) Prog. Theoret. Phys. , vol.85 , pp. 417-421
    • Sakaguchi, H.1
  • 65
    • 0009905308 scopus 로고
    • Stability of phase-singular solutions to one-dimensional complex Ginzburg-Landau equation
    • Sasa S., Iwamoto T. Stability of phase-singular solutions to one-dimensional complex Ginzburg-Landau equation. Phys. Lett. A. 175:1993;289-294.
    • (1993) Phys. Lett. a , vol.175 , pp. 289-294
    • Sasa, S.1    Iwamoto, T.2
  • 66
    • 0000503173 scopus 로고
    • Stability of the Bekki-Nozaki hole solutions to the one-dimensional complex Ginzburg-Landau equation
    • Chaté H., Manneville P. Stability of the Bekki-Nozaki hole solutions to the one-dimensional complex Ginzburg-Landau equation. Phys. Lett. A. 171:1992;183-188.
    • (1992) Phys. Lett. a , vol.171 , pp. 183-188
    • Chaté, H.1    Manneville, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.