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Volumn , Issue 66, 2004, Pages 3559-3584

Asymptotic stability and completeness in the energy space for nonlinear schrödinger equations with small solitary waves

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EID: 12344303082     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804132340     Document Type: Article
Times cited : (93)

References (39)
  • 1
    • 0003655368 scopus 로고
    • Lectures on exponential decay of solutions of second-order elliptic equations: Bounds on eigenfunctions of N-Body Schr̈dinger operators
    • Princeton University Press, New Jersey
    • S. Agmon, Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schr̈dinger Operators, Mathematical Notes, vol. 29, Princeton University Press, New Jersey, 1982.
    • (1982) Mathematical Notes , vol.29
    • Agmon, S.1
  • 3
    • 0000073733 scopus 로고
    • Scattering for the nonlinear Schrödinger equation: States close to a soliton
    • V. S. Buslaev and G. S. Perel'man, Scattering for the nonlinear Schrödinger equation: States close to a soliton, St. Petersburg Math. J. 4 (1993), no. 6, 1111-1142.
    • (1993) St. Petersburg Math. J. , vol.4 , Issue.6 , pp. 1111-1142
    • Buslaev, V.S.1    Perel'man, G.S.2
  • 4
    • 0002779183 scopus 로고
    • On the stability of solitary waves for nonlinear Schrödinger equations
    • American Mathematical Society, Rhode Island
    • _, On the stability of solitary waves for nonlinear Schrödinger equations, Nonlinear Evolution Equations, Amer. Math. Soc. Transl. Ser. 2, vol. 164, American Mathematical Society, Rhode Island, 1995, pp. 75-98.
    • (1995) Nonlinear Evolution Equations, Amer. Math. Soc. Transl. Ser. 2 , vol.164 , pp. 75-98
  • 5
    • 0347495345 scopus 로고    scopus 로고
    • On asymptotic stability of solitary waves for nonlinear Schrödinger equations
    • V. S. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 3, 419-475.
    • (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.20 , Issue.3 , pp. 419-475
    • Buslaev, V.S.1    Sulem, C.2
  • 6
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • T. Cazenave and P.-L. Lions, 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
  • 7
    • 0002191120 scopus 로고
    • Harmonic analysis on semigroups
    • M. G. Cowling, Harmonic analysis on semigroups, Ann. of Math. (2) 117 (1983), no. 2, 267-283.
    • (1983) Ann. of Math. (2) , vol.117 , Issue.2 , pp. 267-283
    • Cowling, M.G.1
  • 8
    • 0035595894 scopus 로고    scopus 로고
    • Stabilization of solutions to nonlinear Schrödinger equations
    • S. Cuccagna, Stabilization of solutions to nonlinear Schrödinger equations, Comm. Pure Appl. Math. 54 (2001), no. 9, 1110-1145.
    • (2001) Comm. Pure Appl. Math. , vol.54 , Issue.9 , pp. 1110-1145
    • Cuccagna, S.1
  • 9
    • 0347633259 scopus 로고    scopus 로고
    • On asymptotic stability of ground states of NLS
    • _, On asymptotic stability of ground states of NLS, Rev. Math. Phys. 15 (2003), no. 8, 877-903.
    • (2003) Rev. Math. Phys. , vol.15 , Issue.8 , pp. 877-903
  • 11
    • 0036101479 scopus 로고    scopus 로고
    • On the point-particle (Newtonian) limit of the non-linear Hartree equation
    • J. Fröhlich, T.-P. Tsai, and H.-T. Yau, On the point-particle (Newtonian) limit of the non-linear Hartree equation, Comm. Math. Phys. 225 (2002), no. 2, 223-274.
    • (2002) Comm. Math. Phys. , vol.225 , Issue.2 , pp. 223-274
    • Fröhlich, J.1    Tsai, T.-P.2    Yau, H.-T.3
  • 12
    • 0001270512 scopus 로고
    • Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations
    • J. Ginibre and G. Velo, Time decay of finite energy solutions of the nonlinear Klein-Gordon and Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 43 (1985), no. 4, 399-442.
    • (1985) Ann. Inst. H. Poincaré Phys. Théor. , vol.43 , Issue.4 , pp. 399-442
    • Ginibre, J.1    Velo, G.2
  • 14
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry. I
    • M. Grillakis, J. Shatah, and W. Strauss, 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
  • 16
    • 84990619685 scopus 로고
    • Decay estimates for Schrödinger operators
    • J.-L. Journé, A. Soffer, and C. D. Sogge, 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
  • 17
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. Math. 120 (1998), no. 5, 955-980.
    • (1998) Amer. J. Math. , vol.120 , Issue.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 18
    • 0035609368 scopus 로고    scopus 로고
    • Asymptotic stability of solitons for subcritical generalized KdV equations
    • Y. Martel and F. Merle, Asymptotic stability of solitons for subcritical generalized KdV equations, Arch. Ration. Mech. Anal. 157 (2001), no. 3, 219-254.
    • (2001) Arch. Ration. Mech. Anal. , vol.157 , Issue.3 , pp. 219-254
    • Martel, Y.1    Merle, F.2
  • 19
    • 0036882736 scopus 로고    scopus 로고
    • Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations
    • Y. Martel, F. Merle, and T.-P. Tsai, Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002), no. 2, 347-373.
    • (2002) Comm. Math. Phys. , vol.231 , Issue.2 , pp. 347-373
    • Martel, Y.1    Merle, F.2    Tsai, T.-P.3
  • 20
    • 0031285644 scopus 로고    scopus 로고
    • Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces
    • M. Nakamura and T. Ozawa, Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces, Rev. Math. Phys. 9 (1997), no. 3, 397-410.
    • (1997) Rev. Math. Phys. , vol.9 , Issue.3 , pp. 397-410
    • Nakamura, M.1    Ozawa, T.2
  • 22
    • 0001322178 scopus 로고    scopus 로고
    • Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations
    • C.-A. Pillet and C. E. Wayne, 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
  • 25
    • 0000173206 scopus 로고
    • On the bound states of the nonlinear Schrödinger equation with a linear potential
    • H. A. Rose and M. I. Weinstein, On the bound states of the nonlinear Schrödinger equation with a linear potential, Phys. D 30 (1988), no. 1-2, 207-218.
    • (1988) Phys. D , vol.30 , Issue.1-2 , pp. 207-218
    • Rose, H.A.1    Weinstein, M.I.2
  • 26
    • 0000301325 scopus 로고
    • Multichannel nonlinear scattering for nonintegrable equations
    • A. Soffer and M. I. Weinstein, 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
    • Soffer, A.1    Weinstein, M.I.2
  • 27
    • 0001641727 scopus 로고
    • Multichannel nonlinear scattering for nonintegrable equations, II. The case of anisotropic potentials and data
    • _, 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
  • 29
    • 0001684804 scopus 로고
    • Nonlinear scattering theory at low energy
    • W. A. Strauss, Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), no. 1, 110-133.
    • (1981) J. Funct. Anal. , vol.41 , Issue.1 , pp. 110-133
    • Strauss, W.A.1
  • 30
    • 12344264373 scopus 로고    scopus 로고
    • On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation
    • to appear in
    • T. Tao, On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation, to appear in J. PDE and Dyn. Sys.
    • J. PDE and Dyn. Sys.
    • Tao, T.1
  • 32
    • 0038349584 scopus 로고    scopus 로고
    • Asymptotic dynamics of nonlinear Schröinger equations with many bound states
    • T.-P. Tsai, Asymptotic dynamics of nonlinear Schröinger equations with many bound states, J. Differential Equations 192 (2003), no. 1, 225-282.
    • (2003) J. Differential Equations , vol.192 , Issue.1 , pp. 225-282
    • Tsai, T.-P.1
  • 33
    • 0036221809 scopus 로고    scopus 로고
    • Asymptotic dynamics of nonlinear Schrödinger equations: Resonancedominated and dispersion-dominated solutions
    • T.-P. Tsai and H.-T. Yau, Asymptotic dynamics of nonlinear Schrödinger equations: resonancedominated and dispersion-dominated solutions, Comm. Pure Appl. Math. 55 (2002), no. 2, 153-216.
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.2 , pp. 153-216
    • Tsai, T.-P.1    Yau, H.-T.2
  • 34
    • 0038707659 scopus 로고    scopus 로고
    • Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data
    • _, Classification of asymptotic profiles for nonlinear Schrödinger equations with small initial data, Adv. Theor. Math. Phys. 6 (2002), no. 1, 107-139.
    • (2002) Adv. Theor. Math. Phys. , vol.6 , Issue.1 , pp. 107-139
  • 35
    • 0036350836 scopus 로고    scopus 로고
    • Relaxation of excited states in nonlinear Schrödinger equations
    • _, Relaxation of excited states in nonlinear Schrödinger equations, Int. Math. Res. Not. 2002 (2002), no. 31, 1629-1673.
    • (2002) Int. Math. Res. Not. , vol.2002 , Issue.31 , pp. 1629-1673
  • 36
    • 0036946822 scopus 로고    scopus 로고
    • Stable directions for excited states of nonlinear Schrödinger equations
    • _, Stable directions for excited states of nonlinear Schrödinger equations, Comm. Partial Differential Equations 27 (2002), no. 11-12, 2363-2402.
    • (2002) Comm. Partial Differential Equations , vol.27 , Issue.11-12 , pp. 2363-2402
  • 37
    • 0034349544 scopus 로고    scopus 로고
    • Center manifold for nonintegrable nonlinear Schrödinger equations on the line
    • R. Weder, 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
  • 38
    • 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, 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
  • 39
    • 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


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