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Volumn 268, Issue 3, 2006, Pages 757-817

Stable directions for small nonlinear dirac standing waves

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EID: 33750380381     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0112-3     Document Type: Article
Times cited : (49)

References (67)
  • 1
    • 0003288140 scopus 로고    scopus 로고
    • 0-groups, commutator methods and spectral theory of N-body Hamiltonians
    • [ABdMG96]. Basel: Birkhäuser Verlag
    • 0-groups, commutator methods and spectral theory of N-body Hamiltonians. Volume 135 of Progress in Mathematics. Basel: Birkhäuser Verlag (1996)
    • (1996) Progress in Mathematics , vol.135
    • Amrein, W.O.1    Boutet De Monvel, A.2    Georgescu, V.3
  • 2
    • 0000815745 scopus 로고
    • Spectral properties of Schrödinger operators and scattering theory
    • [Agm75]
    • [Agm75] Agmon, S.: Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 2(2), 151-218 (1975)
    • (1975) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.2 , Issue.2 , pp. 151-218
    • Agmon, S.1
  • 3
    • 11744323665 scopus 로고
    • Stability of the minimum solitary wave of a nonlinear spinorial model
    • [AS86]
    • [AS86] Alvarez, A., Soler, M.: Stability of the minimum solitary wave of a nonlinear spinorial model. Phys. Rev D 34, 644-645 (1986)
    • (1986) Phys. Rev D , vol.34 , pp. 644-645
    • Alvarez, A.1    Soler, M.2
  • 5
    • 38249012488 scopus 로고
    • Limiting absorption principle and resonances for the Dirac operator
    • [BH92]
    • [BH92] Balslev, E., Helffer, B.: Limiting absorption principle and resonances for the Dirac operator. Adv. Appl. Math. 13(2), 186-215 (1992)
    • (1992) Adv. Appl. Math. , vol.13 , Issue.2 , pp. 186-215
    • Balslev, E.1    Helffer, B.2
  • 7
    • 0002922728 scopus 로고
    • On nonlinear scattering of states which are close to a soliton
    • [BP92b] Nantes
    • [BP92b] Buslaev. V.S., Perel'man, G.S.: On nonlinear scattering of states which are close to a soliton. Méthodes semi-classiques, Vol. 2 (Nantes, (1991)),
    • (1991) Méthodes Semi-classiques , vol.2
    • Buslaev, V.S.1    Perel'man, G.S.2
  • 8
    • 33750359349 scopus 로고
    • Astérisque 210(6), 49-63 (1992)
    • (1992) Astérisque , vol.210 , Issue.6 , pp. 49-63
  • 9
    • 0002189021 scopus 로고
    • Scattering for the nonlinear Schrödinger equation: States that are close to a soliton
    • [BP92c]
    • [BP92c] Buslaev, V.S., Perel'man, G.S.: Scattering for the nonlinear Schrödinger equation: states that are close to a soliton. Algebra i Analiz 4(6), 63-102 (1992)
    • (1992) Algebra i Analiz , vol.4 , Issue.6 , pp. 63-102
    • Buslaev, V.S.1    Perel'Man, G.S.2
  • 10
    • 0002779183 scopus 로고
    • On the stability of solitary waves for nonlinear Schrödinger equations
    • [BP95]. Nonlinear evolution equations, Providence, RI: Amer. Math. Soc.
    • [BP95] Buslaev, V.S., G. S. Perel'man. On the stability of solitary waves for nonlinear Schrödinger equations. In: Nonlinear evolution equations. Volume 164 of Amer. Math. Soc. Transl. Ser. 2, Providence, RI: Amer. Math. Soc., 1995, pp. 75-98
    • (1995) Amer. Math. Soc. Transl. Ser. 2 , vol.164 , pp. 75-98
    • Buslaev, V.S.1    Perel'Man, G.S.2
  • 11
    • 33750331623 scopus 로고
    • p -estimates of difference schemes for strictly hyperbolic systems with nonsmooth data
    • [Bre77]
    • p -estimates of difference schemes for strictly hyperbolic systems with nonsmooth data. SIAM J. Numer. Anal. 14(6), 1126-1144 (1977)
    • (1977) SIAM J. Numer. Anal. , vol.14 , Issue.6 , pp. 1126-1144
    • Brenner, P.1
  • 12
    • 0000185785 scopus 로고
    • On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations
    • [Bre85]
    • [Bre85] Brenner, P.: On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations. J. Differ. Eqs. 56(3), 310-344 (1985)
    • (1985) J. Differ. Eqs. , vol.56 , Issue.3 , pp. 310-344
    • Brenner, P.1
  • 13
    • 33750321903 scopus 로고    scopus 로고
    • Asymptotic stability of solitary waves for nonlinear Schrödinger equations
    • [BS02]. The legacy of the inverse scattering transform in applied mathematics (South Hadley, MA, 2001), Providence, RI: Amer. Math. Soc.
    • [BS02] Buslaev, V.S., Sulem, C.: Asymptotic stability of solitary waves for nonlinear Schrödinger equations. In: The legacy of the inverse scattering transform in applied mathematics (South Hadley, MA, 2001) Vol. 301 of Contemp. Math., Providence, RI: Amer. Math. Soc., 2002 pp. 163-181
    • (2002) Contemp. Math. , vol.301 , pp. 163-181
    • Buslaev, V.S.1    Sulem, C.2
  • 14
    • 0347495345 scopus 로고    scopus 로고
    • On asymptotic stability of solitary waves for nonlinear Schrödinger equations
    • [BS03]
    • [BS03] Buslaev, V.S., Sulem, C.: On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 20(3), 419-475 (2003)
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.3 , pp. 419-475
    • Buslaev, V.S.1    Sulem, C.2
  • 15
    • 4244210911 scopus 로고
    • Stability of nonlinear spinor fields with application to the Gross-Neveu model
    • [BSV87]
    • [BSV87] Blanchard, P., Stubbe, J., Vàzquez, L.: Stability of nonlinear spinor fields with application to the Gross-Neveu model. Phys. Rev. D 36, 2422-2428 (1987)
    • (1987) Phys. Rev. D , vol.36 , pp. 2422-2428
    • Blanchard, P.1    Stubbe, J.2    Vàzquez, L.3
  • 16
    • 0035731981 scopus 로고    scopus 로고
    • Orbital stability and standing waves for the nonlinear Schrödinger equation with potential
    • [CF01]
    • [CF01] Cid, C., Felmer, P.: Orbital stability and standing waves for the nonlinear Schrödinger equation with potential. Rev. Math. Phys. 13(12), 1529-1546 (2001)
    • (2001) Rev. Math. Phys. , vol.13 , Issue.12 , pp. 1529-1546
    • Cid, C.1    Felmer, P.2
  • 17
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • [CL82]
    • [CL82] Cazenave, T., Lions, P.-L.: Orbital stability of standing waves for some nonlinear Schrödinger equations. Commun. Math. Phys. 85(4), 549-561 (1982)
    • (1982) Commun. Math. Phys. , vol.85 , Issue.4 , pp. 549-561
    • Cazenave, T.1    Lions, P.-L.2
  • 18
    • 0035579999 scopus 로고    scopus 로고
    • On the wave equation with a magnetic potential
    • [CS01]
    • [CS01] Cuccagna, S., Schirmer, P.P.: On the wave equation with a magnetic potential. Comm. Pure Appl. Math. 54(2), 135-152 (2001)
    • (2001) Comm. Pure Appl. Math. , vol.54 , Issue.2 , pp. 135-152
    • Cuccagna, S.1    Schirmer, P.P.2
  • 19
    • 0035595894 scopus 로고    scopus 로고
    • Stabilization of solutions to nonlinear Schrödinger equations
    • [Cuc01]
    • [Cuc01] Cuccagna, S.: Stabilization of solutions to nonlinear Schrödinger equations. Comm. Pure Appl. Math. 54(9), 1110-1145 (2001)
    • (2001) Comm. Pure Appl. Math. , vol.54 , Issue.9 , pp. 1110-1145
    • Cuccagna, S.1
  • 20
    • 0347633259 scopus 로고    scopus 로고
    • On asymptotic stability of ground states of NLS
    • [Cuc03]
    • [Cuc03] Cuccagna, S.: On asymptotic stability of ground states of NLS. Rev. Math. Phys. 15(8), 877-903 (2003)
    • (2003) Rev. Math. Phys. , vol.15 , Issue.8 , pp. 877-903
    • Cuccagna, S.1
  • 21
    • 19744362218 scopus 로고    scopus 로고
    • Erratum: "Stabilization of solutions to nonlinear Schrödinger equations" Comm. Pure Appl. Math. 54(9), 1110-1145 (2001)
    • [Cuc05]
    • [Cuc05] Cuccagna, S.: Erratum: "Stabilization of solutions to nonlinear Schrödinger equations" [Comm. Pure Appl. Math. 54(9), 1110-1145 (2001). Comm. Pure Appl. Math. 58(1), 147 (2005)
    • (2005) Comm. Pure Appl. Math. , vol.58 , Issue.1 , pp. 147
    • Cuccagna, S.1
  • 22
    • 33846659919 scopus 로고    scopus 로고
    • Decay estimates for the wave and dirac equations with a magnetic potential
    • [DF] To appear on
    • [DF] D'Ancona, P., Fanelli, L.: Decay estimates for the wave and dirac equations with a magnetic potential. To appear on Comm. Pure Appl. Math.
    • Comm. Pure Appl. Math.
    • D'Ancona, P.1    Fanelli, L.2
  • 23
    • 24144498202 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. i
    • [ES04]
    • [ES04] Erdoǧan, M.B., Schlag, W.: Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three. I. Dyn. Partial Differ. Eq. 1(4), 359-379 (2004)
    • (2004) Dyn. Partial Differ. Eq. , vol.1 , Issue.4 , pp. 359-379
    • Erdoǧan, M.B.1    Schlag, W.2
  • 25
    • 7544247538 scopus 로고    scopus 로고
    • Zero energy asymptotics of the resolvent for a class of slowly decaying potentials
    • [FS04]
    • [FS04] Fournais, S., Skibsted, E. : Zero energy asymptotics of the resolvent for a class of slowly decaying potentials. Math. Z. 248(3), 593-633 (2004)
    • (2004) Math. Z. , vol.248 , Issue.3 , pp. 593-633
    • Fournais, S.1    Skibsted, E.2
  • 26
    • 0041077496 scopus 로고    scopus 로고
    • On the spectral theory of singular Dirac type Hamiltonians
    • [GM01]
    • [GM01] Georgescu, V., Mǎntoiu, M.: On the spectral theory of singular Dirac type Hamiltonians. J. Operator Theory 46(2), 289-321 (2001)
    • (2001) J. Operator Theory , vol.46 , Issue.2 , pp. 289-321
    • Georgescu, V.1    Mǎntoiu, M.2
  • 27
    • 12344303082 scopus 로고    scopus 로고
    • Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves
    • [GNT04]
    • [GNT04] Gustafson, S., Nakanishi, K., Tsai, T.-P: Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves. Int. Math. Res. Not. 66, 3559-3584 (2004)
    • (2004) Int. Math. Res. Not. , vol.66 , pp. 3559-3584
    • Gustafson, S.1    Nakanishi, K.2    Tsai, T.-P.3
  • 29
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry. 1
    • [GSS87]
    • [GSS87] Grillakis, M., Shatah, J., Strauss, W.: Stability theory of solitary waves in the presence of symmetry. 1. J. Funct. Anal. 74(1), 160-197 (1987)
    • (1987) J. Funct. Anal. , vol.74 , Issue.1 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 30
    • 0012939763 scopus 로고    scopus 로고
    • Exponential decay of two-body eigenfunctions: A review
    • [His00] Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley. CA. 1999) (electronic)
    • [His00] Hislop, P.D.: Exponential decay of two-body eigenfunctions: a review. In: Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley. CA. 1999) Volume 4 of Electron. J. Differ. Eq. Conf. pp 265-288 (electronic)
    • Electron. J. Differ. Eq. Conf. , vol.4 , pp. 265-288
    • Hislop, P.D.1
  • 31
    • 0034376103 scopus 로고    scopus 로고
    • Time-dependent scattering theory of W-body quantum systems
    • [HS00]
    • [HS00] Hunziker, W., Sigal, I.M.: Time-dependent scattering theory of W-body quantum systems. Rev. Math. Phys. 12(8), 1033-1084 (2000)
    • (2000) Rev. Math. Phys. , vol.12 , Issue.8 , pp. 1033-1084
    • Hunziker, W.1    Sigal, I.M.2
  • 33
    • 0041782176 scopus 로고    scopus 로고
    • Limiting absorption principle at critical values for the Dirac operator
    • [IM99]
    • [IM99] Iftimovici, A., Mantoiu, M.: Limiting absorption principle at critical values for the Dirac operator. Lett. Math. Phys. 49(3), 235-243 (1999)
    • (1999) Lett. Math. Phys. , vol.49 , Issue.3 , pp. 235-243
    • Iftimovici, A.1    Mantoiu, M.2
  • 34
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • [JK79]
    • [JK79] Jensen, A., Kato, T.: Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46(3), 583-611 (1979)
    • (1979) Duke Math. J. , vol.46 , Issue.3 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 35
    • 0035619840 scopus 로고    scopus 로고
    • A unified approach to resolvent expansions at thresholds
    • [JN01]
    • [JN01] Jensen, A., Nenciu, G.: A unified approach to resolvent expansions at thresholds. Rev. Math. Phys. 13(6), 717-754 (2001)
    • (2001) Rev. Math. Phys. , vol.13 , Issue.6 , pp. 717-754
    • Jensen, A.1    Nenciu, G.2
  • 36
    • 13844264249 scopus 로고    scopus 로고
    • Erratum: "A unified approach to resolvent expansions at thresholds" [Rev. Math. Phys. 16(6), 717-754 (2001)]
    • [JN04]
    • [JN04] Jensen, A., Nenciu, G.: Erratum: "A unified approach to resolvent expansions at thresholds" [Rev. Math. Phys. 16(6), 717-754 (2001)]. Rev. Math. Phys. 16(5), 675-677 (2004)
    • (2004) Rev. Math. Phys. , vol.16 , Issue.5 , pp. 675-677
    • Jensen, A.1    Nenciu, G.2
  • 37
    • 84990619685 scopus 로고
    • Decay estimates for Schrödinger operators
    • [JSS91]
    • [JSS91] Journé, J.-L., Soffer, A., Sogge, CD.: Decay estimates for Schrödinger operators. Comm. Pure Appl. Math. 44(5), 573-604 (1991)
    • (1991) Comm. Pure Appl. Math. , vol.44 , Issue.5 , pp. 573-604
    • Journé, J.-L.1    Soffer, A.2    Sogge, C.D.3
  • 38
    • 0000570999 scopus 로고
    • Wave operators and similarity for some non-selfadjoint operators
    • [Kat66]
    • [Kat66] Kato, T.: Wave operators and similarity for some non-selfadjoint operators. Math. Ann. 162, 258-279 (1965/1966)
    • (1965) Math. Ann. , vol.162 , pp. 258-279
    • Kato, T.1
  • 42
    • 29144474094 scopus 로고
    • Résonances paires pour l'opérateur de Dirac
    • [Par90]
    • [Par90] Parisse, B.: Résonances paires pour l'opérateur de Dirac. C. R. Acad. Sci. Paris Sér. I. Math. 310(5), 265-268 (1990)
    • (1990) C. R. Acad. Sci. Paris Sér. I. Math. , vol.310 , Issue.5 , pp. 265-268
    • Parisse, B.1
  • 43
    • 0001322178 scopus 로고    scopus 로고
    • Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
    • [PW97]
    • [PW97] Pillet, C.-A., Wayne, C.E.: Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations. J. Differ. Eqs. 141(2), 310-326 (1997)
    • (1997) J. Differ. Eqs. , vol.141 , Issue.2 , pp. 310-326
    • Pillet, C.-A.1    Wayne, C.E.2
  • 44
    • 0007586781 scopus 로고
    • Classical nonlinear dirac field models of extended particles
    • [Ran], A. O. Barut, ed., Amsterdam: Reidel
    • [Ran] Ranada, A.F.: Classical nonlinear dirac field models of extended particles. In: Quantum Theory, Groups, Fields and Particles. Volume 198, A. O. Barut, ed., Amsterdam: Reidel, 1983, pp. 271-291
    • (1983) Quantum Theory, Groups, Fields and Particles , vol.198 , pp. 271-291
    • Ranada, A.F.1
  • 45
    • 0003276274 scopus 로고
    • Methods of modern mathematical physics. IV
    • [RS78]. New York: Academic Press [Harcourt Brace Jovanovich Publishers]
    • [RS78] Reed, M., Simon, B.: Methods of Modern Mathematical Physics. IV. Analysis of operators. New York: Academic Press [Harcourt Brace Jovanovich Publishers], (1978)
    • (1978) Analysis of Operators
    • Reed, M.1    Simon, B.2
  • 46
    • 0003937747 scopus 로고
    • [RS79]. New York: Academic Press [Harcourt Brace Jovanovich Publishers]
    • [RS79] Reed, M., Simon, B.: Methods of Modern Mathematical Physics. III. New York: Academic Press [Harcourt Brace Jovanovich Publishers], 1979
    • (1979) Methods of Modern Mathematical Physics , vol.3
    • Reed, M.1    Simon, B.2
  • 48
    • 11844298384 scopus 로고    scopus 로고
    • Dispersive analysis of charge transfer models
    • [RSS05b]
    • [RSS05b] Rodnianski, I., Schlag, W., Soffer, A.: Dispersive analysis of charge transfer models. Comm. Pure Appl. Math. 58(2), 149-216 (2005)
    • (2005) Comm. Pure Appl. Math. , vol.58 , Issue.2 , pp. 149-216
    • Rodnianski, I.1    Schlag, W.2    Soffer, A.3
  • 51
    • 0001420204 scopus 로고
    • Instability of nonlinear bound states
    • [SS85]
    • [SS85] Shatah, J., Strauss, W.: Instability of nonlinear bound states. Commun. Math. Phys. 100(2), 173-190 (1985)
    • (1985) Commun. Math. Phys. , vol.100 , Issue.2 , pp. 173-190
    • Shatah, J.1    Strauss, W.2
  • 53
    • 4244211971 scopus 로고
    • Stability under dilations of nonlinear spinor fields
    • [SV86]
    • [SV86] Strauss, W.A., Vázquez, L.: Stability under dilations of nonlinear spinor fields. Phys. Rev. D 34, 641-643 (1986)
    • (1986) Phys. Rev. D , vol.34 , pp. 641-643
    • Strauss, W.A.1    Vázquez, L.2
  • 54
    • 0000301325 scopus 로고
    • Multichannel nonlinear scattering for nonintegrable equations
    • [SW90]
    • [SW90] Soffer, A., Weinstein, M.I.: Multichannel nonlinear scattering for nonintegrable equations. Commun. Math. Phys. 133(1), 119-146 (1990)
    • (1990) Commun. Math. Phys. , vol.133 , Issue.1 , pp. 119-146
    • Soffer, A.1    Weinstein, M.I.2
  • 55
    • 0001641727 scopus 로고
    • Multichannel nonlinear scattering for nonintegrable equations. II. The case of anisotropic potentials and data
    • [SW92]
    • [SW92] Soffer, A., Weinstein, M.I.: Multichannel nonlinear scattering for nonintegrable equations. II. The case of anisotropic potentials and data. J. Differ. Eqs. 98(2), 376-390 (1992)
    • (1992) J. Differ. Eqs. , vol.98 , Issue.2 , pp. 376-390
    • Soffer, A.1    Weinstein, M.I.2
  • 56
    • 0033460613 scopus 로고    scopus 로고
    • Resonances, radiation damping and instability in Hamiltonian nonlinear' wave equations
    • [SW99]
    • [SW99] Soffer, A., Weinstein, M.I.: Resonances, radiation damping and instability in Hamiltonian nonlinear' wave equations. Invent. Math. 136(1), 9-74 (1999)
    • (1999) Invent. Math. , vol.136 , Issue.1 , pp. 9-74
    • Soffer, A.1    Weinstein, M.I.2
  • 57
    • 12144269880 scopus 로고    scopus 로고
    • Selection of the ground state for nonlinear Schrödinger equations
    • [SW04]
    • [SW04] Soffer, A., Weinstein, M.I.: Selection of the ground state for nonlinear Schrödinger equations. Rev. Math. Phys. 16(8), 977-1071 (2004)
    • (2004) Rev. Math. Phys. , vol.16 , Issue.8 , pp. 977-1071
    • Soffer, A.1    Weinstein, M.I.2
  • 58
    • 28844490887 scopus 로고    scopus 로고
    • Theory of nonlinear dispersive waves and selection of the ground state
    • [SW05]
    • [SW05] Soffer, A., Weinstein, M.I.: Theory of Nonlinear Dispersive Waves and Selection of the Ground State. Phys. Rev. Lett. 95(21), 213905 (2005)
    • (2005) Phys. Rev. Lett. , vol.95 , Issue.21 , pp. 213905
    • Soffer, A.1    Weinstein, M.I.2
  • 60
    • 0038349584 scopus 로고    scopus 로고
    • Asymptotic dynamics of nonlinear Schrödinger equations with many bound states
    • [Tsa03]
    • [Tsa03] Tsai, T.-P: Asymptotic dynamics of nonlinear Schrödinger equations with many bound states. J. Differ. Eqs. 192(1), 225-282 (2003)
    • (2003) J. Differ. Eqs. , vol.192 , Issue.1 , pp. 225-282
    • Tsai, T.-P.1
  • 61
    • 0036221809 scopus 로고    scopus 로고
    • Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions
    • [TY02a]
    • [TY02a] Tsai, T.-P, Yau, H.-T.: Asymptotic dynamics of nonlinear Schrödinger equations: resonance-dominated and dispersion-dominated solutions. Comm. Pure Appl. Math. 55(2), 153-216 (2002)
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.2 , pp. 153-216
    • Tsai, T.-P.1    Yau, H.-T.2
  • 62
    • 0038707659 scopus 로고    scopus 로고
    • Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data
    • [TY02b]
    • [TY02b] Tsai, T.-P., Yau, H.-T.: Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data. Adv. Theor. Math. Phys. 6(1), 107-139 (2002)
    • (2002) Adv. Theor. Math. Phys. , vol.6 , Issue.1 , pp. 107-139
    • Tsai, T.-P.1    Yau, H.-T.2
  • 63
    • 0036350836 scopus 로고    scopus 로고
    • Relaxation of excited states in nonlinear Schrödinger equations
    • [TY02c]
    • [TY02c] Tsai, T.-P., Yau, H.-T.: Relaxation of excited states in nonlinear Schrödinger equations. Int. Math. Res. Not. 31, 1629-1673 (2002)
    • (2002) Int. Math. Res. Not. , vol.31 , pp. 1629-1673
    • Tsai, T.-P.1    Yau, H.-T.2
  • 64
    • 0036946822 scopus 로고    scopus 로고
    • Stable directions for excited states of nonlinear Schrödinger equations
    • [TY02d]
    • [TY02d] Tsai, T.-P, Yau, H.-T.: Stable directions for excited states of nonlinear Schrödinger equations. Comm. Partial Differ. Eqs. 27(11-12), 2363-2402 (2002)
    • (2002) Comm. Partial Differ. Eqs. , vol.27 , Issue.11-12 , pp. 2363-2402
    • Tsai, T.-P.1    Yau, H.-T.2
  • 65
    • 0034349544 scopus 로고    scopus 로고
    • Center manifold for nonintegrable nonlinear Schrödinger equations on the line
    • [Wed00]
    • [Wed00] Weder, R.: Center manifold for nonintegrable nonlinear Schrödinger equations on the line. Commun. Math. Phys. 215(2), 343-356 (2000)
    • (2000) Commun. Math. Phys. , vol.215 , Issue.2 , pp. 343-356
    • Weder, R.1
  • 66
    • 84972559697 scopus 로고
    • k,p-continuity of wave operators for Schrödinger operators
    • [Yaj95]
    • k,p-continuity of wave operators for Schrödinger operators. J. Math. Soc. Japan 47(3), 551-581 (1995)
    • (1995) J. Math. Soc. Japan , vol.47 , Issue.3 , pp. 551-581
    • Yajima, K.1
  • 67
    • 0039962313 scopus 로고
    • A remark on the limiting absorption method for Dirac operators
    • [Yam93]
    • [Yam93] Yamada, O.: A remark on the limiting absorption method for Dirac operators. Proc. Japan Acad. Ser. A Mam. Sci. 69(7), 243-246 (1993)
    • (1993) Proc. Japan Acad. Ser. A Mam. Sci. , vol.69 , Issue.7 , pp. 243-246
    • Yamada, O.1


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