메뉴 건너뛰기




Volumn 54, Issue 9, 2001, Pages 1110-1145

Stabilization of solutions to nonlinear Schrödinger equations

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0035595894     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.1018     Document Type: Article
Times cited : (149)

References (43)
  • 1
    • 0040275794 scopus 로고    scopus 로고
    • p-continuity of wave operators for one dimensional Schrödinger operators
    • p-continuity of wave operators for one dimensional Schrödinger operators. J. Math. Sci. Univ. Tokyo 7 (2000), no. 2, 221-240.
    • (2000) J. Math. Sci. Univ. Tokyo , vol.7 , Issue.2 , pp. 221-240
    • Artbazar, G.1    Yajima, K.2
  • 2
    • 0000817006 scopus 로고
    • Instabilité des états stationnaires dans les équations de schrödinger et de klein-gordon non linéaires
    • Berestycki, H.; Cazenave, T. Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires. C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 9, 489-492.
    • (1981) C. R. Acad. Sci. Paris Sér. I Math. , vol.293 , Issue.9 , pp. 489-492
    • Berestycki, H.1    Cazenave, T.2
  • 3
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations. I. Existence of a ground state
    • Berestycki, H.; Lions, P.-L. Nonlinear scalar field equations. I. Existence of a ground state. Arch. Rational Mech. Anal. 82 (1983), no. 4, 313-345.
    • (1983) Arch. Rational Mech. Anal. , vol.82 , Issue.4 , pp. 313-345
    • Berestycki, H.1    Lions, P.-L.2
  • 4
    • 0002189021 scopus 로고
    • Scattering for the nonlinear Schrödinger equation: States that are close to a soliton
    • Buslaev, V. S.; Perel'man, G. S. Scattering for the nonlinear Schrödinger equation: states that are close to a soliton. Algebra i Analiz 4 (1992), no. 6, 63-102; translation in St. Petersburg Math. J. 4 (1993), no. 6, 1111-1142.
    • (1992) Algebra I Analiz , vol.4 , Issue.6 , pp. 63-102
    • Buslaev, V.S.1    Perel'man, G.S.2
  • 5
    • 0000073733 scopus 로고
    • translation in
    • Buslaev, V. S.; Perel'man, G. S. Scattering for the nonlinear Schrödinger equation: states that are close to a soliton. Algebra i Analiz 4 (1992), no. 6, 63-102; translation in St. Petersburg Math. J. 4 (1993), no. 6, 1111-1142.
    • (1993) St. Petersburg Math. J. , vol.4 , Issue.6 , pp. 1111-1142
  • 6
    • 0002779183 scopus 로고
    • On the stability of solitary waves for nonlinear Schrödinger equations
    • Nonlinear evolution equations, 75-98. Series 2, American Mathematical Society, Providence, R.I.
    • Buslaev, V. S.; Perel'man, G. S. On the stability of solitary waves for nonlinear Schrödinger equations. Nonlinear evolution equations, 75-98. American Mathematical Society Translations, Series 2, 164. American Mathematical Society, Providence, R.I., 1995.
    • (1995) American Mathematical Society Translations , pp. 164
    • Buslaev, V.S.1    Perel'man, G.S.2
  • 7
    • 0039683992 scopus 로고
    • Stable solutions of the logarithmic Schrödinger equation
    • Cazenave, T. Stable solutions of the logarithmic Schrödinger equation. Nonlinear Anal. 7 (1983), no. 10, 1127-1140.
    • (1983) Nonlinear Anal. , vol.7 , Issue.10 , pp. 1127-1140
    • Cazenave, T.1
  • 8
    • 0003255150 scopus 로고    scopus 로고
    • An introduction to semilinear evolution equations
    • Translated from the 1990 French original by Yvan Martel and revised by the authors. Clarendon, Oxford University Press, New York
    • Cazenave, T.; Haraux, A. An introduction to semilinear evolution equations. Translated from the 1990 French original by Yvan Martel and revised by the authors. Oxford Lecture Series in Mathematics and Its Applications, 13. Clarendon, Oxford University Press, New York, 1998.
    • (1998) Oxford Lecture Series in Mathematics and its Applications , pp. 13
    • Cazenave, T.1    Haraux, A.2
  • 9
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • Cazenave, T.; Lions, P.-L. Orbital stability of standing waves for some nonlinear Schrödinger equations. Comm. Math. Phys. 85 (1982), no. 4, 549-561.
    • (1982) Comm. Math. Phys. , vol.85 , Issue.4 , pp. 549-561
    • Cazenave, T.1    Lions, P.-L.2
  • 12
    • 84990623184 scopus 로고
    • Linearized instability for nonlinear Schrödinger and Klein-Gordon equations
    • Grillakis, M. Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Comm. Pure Appl. Math. 41 (1988), no. 6, 747-774.
    • (1988) Comm. Pure Appl. Math. , vol.41 , Issue.6 , pp. 747-774
    • Grillakis, M.1
  • 13
    • 84990563336 scopus 로고
    • Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system
    • Grillakis, M. Analysis of the linearization around a critical point of an infinite-dimensional Hamiltonian system. Comm. Pure Appl. Math. 43 (1990), no. 3, 299-333.
    • (1990) Comm. Pure Appl. Math. , vol.43 , Issue.3 , pp. 299-333
    • Grillakis, M.1
  • 14
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry. I
    • Grillakis, M.; Shatah, J.; Strauss, W. Stability theory of solitary waves in the presence of symmetry. I. J. Funct. Anal. 74 (1987). no. 1, 160-197.
    • (1987) J. Funct. Anal. , vol.74 , Issue.1 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 15
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry. II
    • Grillakis, M.; Shatah, J.; Strauss, W. Stability theory of solitary waves in the presence of symmetry. II. J. Funct. Anal. 94 (1990), no. 2, 308-348.
    • (1990) J. Funct. Anal. , vol.94 , Issue.2 , pp. 308-348
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 16
    • 0038974528 scopus 로고
    • Nonlinear Schrödinger equations in weighted Sobolev spaces
    • Hayashi, N.; Nakamitsu, K.; Tsutsumi, M. Nonlinear Schrödinger equations in weighted Sobolev spaces. Funkcial. Ekvac. 31 (1988), no. 3, 363-381.
    • (1988) Funkcial. Ekvac. , vol.31 , Issue.3 , pp. 363-381
    • Hayashi, N.1    Nakamitsu, K.2    Tsutsumi, M.3
  • 17
    • 84972562665 scopus 로고
    • m), m ≥ 5
    • m), m ≥ 5. Duke Math. J. 47 (1980), no. 1, 57-80.
    • (1980) Duke Math. J. , vol.47 , Issue.1 , pp. 57-80
    • Jensen, A.1
  • 19
    • 0001016945 scopus 로고
    • d) for the Schrödinger equation with a time-dependent potential
    • d) for the Schrödinger equation with a time-dependent potential. Math. Ann. 299 (1994), no. 1, 117-125.
    • (1994) Math. Ann. , vol.299 , Issue.1 , pp. 117-125
    • Jensen, A.1
  • 20
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • Jensen, A.; Kato, T. Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46 (1979), no. 3, 583-611.
    • (1979) Duke Math. J. , vol.46 , Issue.3 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 21
    • 84990619685 scopus 로고
    • Decay estimates for Schrödinger operators
    • Journé, J.-L.; Soffer, A.; Sogge, C. D. Decay estimates for Schrödinger operators. Comm. Pure Appl. Math. 44 (1991), no. 5, 573-604.
    • (1991) Comm. Pure Appl. Math. , vol.44 , Issue.5 , pp. 573-604
    • Journé, J.-L.1    Soffer, A.2    Sogge, C.D.3
  • 22
    • 84980081672 scopus 로고
    • Growth properties of solutions of the reduced wave equation with a variable coefficient
    • Kato, T. Growth properties of solutions of the reduced wave equation with a variable coefficient. Comm. Pure Appl. Math. 12 (1959), 403-425.
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 403-425
    • Kato, T.1
  • 23
    • 0000570999 scopus 로고
    • Wave operators and similarity for some non-selfadjoint operators
    • Kato, T. Wave operators and similarity for some non-selfadjoint operators. Math. Ann. 162 (1965/1966), 258-279.
    • (1965) Math. Ann. , vol.162 , pp. 258-279
    • Kato, T.1
  • 24
    • 0008112282 scopus 로고
    • Perturbation theory for linear operators
    • Reprint of the 1980 edition. Springer, Berlin
    • Kato, T. Perturbation theory for linear operators. Reprint of the 1980 edition. Classics in Mathematics. Springer, Berlin, 1995.
    • (1995) Classics in Mathematics
    • Kato, T.1
  • 26
    • 0002087150 scopus 로고
    • Asymptotic expansions in time for solutions of Schrödinger-type equations
    • Murata, M. Asymptotic expansions in time for solutions of Schrödinger-type equations. J. Funct. Anal. 49 (1982), no. 1, 10-56.
    • (1982) J. Funct. Anal. , vol.49 , Issue.1 , pp. 10-56
    • Murata, M.1
  • 27
    • 0001322178 scopus 로고    scopus 로고
    • Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
    • Pillet, C.-A.; Wayne, C. E. Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. J. Differential Equations 141 (1997), no. 2, 310-326.
    • (1997) J. Differential Equations , vol.141 , Issue.2 , pp. 310-326
    • Pillet, C.-A.1    Wayne, C.E.2
  • 28
    • 0000229397 scopus 로고
    • Stable standing waves of nonlinear Klein-Gordon equations
    • Shatah, J. Stable standing waves of nonlinear Klein-Gordon equations. Comm. Math. Phys. 91 (1983), no. 3, 313-327.
    • (1983) Comm. Math. Phys. , vol.91 , Issue.3 , pp. 313-327
    • Shatah, J.1
  • 29
    • 0001420204 scopus 로고
    • Instability of nonlinear bound states
    • Shatah, J.; Strauss, W. Instability of nonlinear bound states. Comm. Math. Phys. 100 (1985), no. 2, 173-190.
    • (1985) Comm. Math. Phys. , vol.100 , Issue.2 , pp. 173-190
    • Shatah, J.1    Strauss, W.2
  • 30
    • 0000301325 scopus 로고
    • Multichannel nonlinear scattering for nonintegrable equations
    • Softer, A.; Weinstein, M. I. Multichannel nonlinear scattering for nonintegrable equations. Comm. Math. Phys. 133 (1990), no. 1, 119-146.
    • (1990) Comm. Math. Phys. , vol.133 , Issue.1 , pp. 119-146
    • Softer, A.1    Weinstein, M.I.2
  • 31
    • 0001641727 scopus 로고
    • Multichannel nonlinear scattering for nonintegrable equations. II. The case of anisotropic potentials and data
    • Soffer, A.; Weinstein, M. I. Multichannel nonlinear scattering for nonintegrable equations. II. The case of anisotropic potentials and data. J. Differential Equations 98 (1992), no. 2, 376-390.
    • (1992) J. Differential Equations , vol.98 , Issue.2 , pp. 376-390
    • Soffer, A.1    Weinstein, M.I.2
  • 32
    • 0035218466 scopus 로고    scopus 로고
    • Modulational approach to stability of non-topological solitons in semilinear wave equations
    • Stuart, D. M. A. Modulational approach to stability of non-topological solitons in semilinear wave equations. J. Math. Pures Appl. (9) 80 (2001), no. 1, 51-83.
    • (2001) J. Math. Pures Appl. (9) , vol.80 , Issue.1 , pp. 51-83
    • Stuart, D.M.A.1
  • 33
    • 0003230098 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation. Self-focusing and wave collapse
    • Springer, New York
    • Sulem, C.; Sulem, P.-L. The nonlinear Schrödinger equation. Self-focusing and wave collapse. Applied Mathematical Sciences, 139. Springer, New York, 1999.
    • (1999) Applied Mathematical Sciences , pp. 139
    • Sulem, C.1    Sulem, P.-L.2
  • 35
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • Weinstein, M. I. Modulational stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 16 (1985), no. 3, 472-491.
    • (1985) SIAM J. Math. Anal. , vol.16 , Issue.3 , pp. 472-491
    • Weinstein, M.I.1
  • 36
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • Weinstein, M. I. Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math. 39 (1986), no. 1, 51-67.
    • (1986) Comm. Pure Appl. Math. , vol.39 , Issue.1 , pp. 51-67
    • Weinstein, M.I.1
  • 37
    • 22244488372 scopus 로고    scopus 로고
    • Asymptotic stability of nonlinear bound states in conservative dispersive systems
    • Mathematical problems in the theory of water waves (Luminy, 1995), 223-235. American Mathematical Society, Providence, R.I.
    • Weinstein, M. I. Asymptotic stability of nonlinear bound states in conservative dispersive systems. Mathematical problems in the theory of water waves (Luminy, 1995), 223-235. Contemporary Mathematics, 200. American Mathematical Society, Providence, R.I., 1996.
    • (1996) Contemporary Mathematics , pp. 200
    • Weinstein, M.I.1
  • 38
    • 0033235140 scopus 로고    scopus 로고
    • k,p-continuity of the Schrödinger wave operators on the line
    • k,p-continuity of the Schrödinger wave operators on the line. Comm. Math. Phys. 208 (1999), no. 2, 507-520.
    • (1999) Comm. Math. Phys. , vol.208 , Issue.2 , pp. 507-520
    • Weder, R.1
  • 39
    • 0034349544 scopus 로고    scopus 로고
    • Center manifold for nonintegrable nonlinear Schrödinger equations on the line
    • Weder, R. Center manifold for nonintegrable nonlinear Schrödinger equations on the line. Comm. Math. Phys. 215 (2000), no. 2, 343-356.
    • (2000) Comm. Math. Phys. , vol.215 , Issue.2 , pp. 343-356
    • Weder, R.1
  • 40
    • 0002283169 scopus 로고    scopus 로고
    • p estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
    • p estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential. J. Funct. Anal. 170 (2000), no. 1, 37-68.
    • (2000) J. Funct. Anal. , vol.170 , Issue.1 , pp. 37-68
    • Weder, R.1
  • 41
    • 84972559697 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators
    • k,p-continuity of wave operators for Schrödinger operators. J. Math. Soc. Japan 47 (1995), no. 3, 551-581.
    • (1995) J. Math. Soc. Japan , vol.47 , Issue.3 , pp. 551-581
    • Yajima, K.1
  • 42
    • 0001604108 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators. III. Even-dimensional cases m ≥ 4
    • k,p-continuity of wave operators for Schrödinger operators. III. Even-dimensional cases m ≥ 4. J. Math. Sci. Univ. Tokyo 2 (1995), no. 2, 311-346.
    • (1995) J. Math. Sci. Univ. Tokyo , vol.2 , Issue.2 , pp. 311-346
    • Yajima, K.1
  • 43
    • 0033235580 scopus 로고    scopus 로고
    • p-boundedness of wave operators for two-dimensional Schrödinger operators
    • p-boundedness of wave operators for two-dimensional Schrödinger operators. Comm. Math. Phys. 208 (1999), no. 1, 125-152.
    • (1999) Comm. Math. Phys. , vol.208 , Issue.1 , pp. 125-152
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.