메뉴 건너뛰기




Volumn 29, Issue 7-8, 2004, Pages 1051-1095

Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations

Author keywords

Asymptotic stability; Nonlinear Schr dinger equation; Solitons

Indexed keywords


EID: 8744309907     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-200033754     Document Type: Article
Times cited : (75)

References (36)
  • 1
    • 0002830401 scopus 로고
    • Adiabatic theorems and applications to the quantum hall effect
    • Avron, J. E., Seiler, R., Yaffe, L. G. (1987). Adiabatic theorems and applications to the quantum hall effect. Comm. Math. Phys. 110:33-49.
    • (1987) Comm. Math. Phys. , vol.110 , pp. 33-49
    • Avron, J.E.1    Seiler, R.2    Yaffe, L.G.3
  • 2
    • 0000363750 scopus 로고
    • The stability of solitary waves
    • Benjamin, T. B. (1972). The stability of solitary waves. Proc. Roy. Soc. Lond. A328:153-183.
    • (1972) Proc. Roy. Soc. Lond. , vol.A328 , pp. 153-183
    • Benjamin, T.B.1
  • 3
    • 0020591567 scopus 로고
    • Nonlinear scalar field equations, I, II
    • Berestycki, H., Lions, P.-L. (1983). Nonlinear scalar field equations, I, II. Arch. Rat. Mech. Anal. 82(4):313-375.
    • (1983) Arch. Rat. Mech. Anal. , vol.82 , Issue.4 , pp. 313-375
    • Berestycki, H.1    Lions, P.-L.2
  • 4
    • 0000073733 scopus 로고
    • Scattering for the nonlinear Schrödinger equation: States close to a soliton
    • Buslaev, V. S., Perelman, G. S. (1993). Scattering for the nonlinear Schrödinger equation: States close to a soliton. St. Petersburg Math. J. 4(6):1111-1143.
    • (1993) St. Petersburg Math. J. , vol.4 , Issue.6 , pp. 1111-1143
    • Buslaev, V.S.1    Perelman, G.S.2
  • 5
    • 0002779183 scopus 로고
    • On the stability of solitary waves for nonlinear Schrödinger equation
    • Buslaev, V. S., Perelman, G. S. (1995). On the stability of solitary waves for nonlinear Schrödinger equation. Amer. Math. Soc. Transl. (2) 164:75-99.
    • (1995) Amer. Math. Soc. Transl. (2) , vol.164 , pp. 75-99
    • Buslaev, V.S.1    Perelman, G.S.2
  • 6
    • 0347495345 scopus 로고    scopus 로고
    • On the asymptotic stability of solitary waves of nonlinear Schrödinger equations
    • Buslaev, V. S., Sulem, C. (2003). On the asymptotic stability of solitary waves of nonlinear Schrödinger equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire 20(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
  • 7
    • 0000090159 scopus 로고
    • Orbital stability of standing waves for some nonlinear Schrödinger equations
    • Cazenave, T., Lions, P.-L. (1982). Orbital stability of standing waves for some nonlinear Schrödinger equations. Comm. Math. Phys. 85(4):549-561.
    • (1982) Comm. Math. Phys. , vol.85 , Issue.4 , pp. 549-561
    • Cazenave, T.1    Lions, P.-L.2
  • 8
    • 0035595894 scopus 로고    scopus 로고
    • Stabilization of solutions to nonlinear Schrödinger equation
    • Cuccagna, S. (2001). Stabilization of solutions to nonlinear Schrödinger equation. Comm. Pure Appl. Math. 54:1110-1145.
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 1110-1145
    • Cuccagna, S.1
  • 10
    • 0001274054 scopus 로고
    • On a class of nonlinear Schrödinger equations III
    • Ginibre, J., Velo, G. (1978). On a class of nonlinear Schrödinger equations III. Ann. Inst. H. Poincare -Phys. Theory 28(3):287-316.
    • (1978) Ann. Inst. H. Poincare -Phys. Theory , vol.28 , Issue.3 , pp. 287-316
    • Ginibre, J.1    Velo, G.2
  • 11
    • 0002172263 scopus 로고
    • On a class of nonlinear Schrödinger equations I, II
    • Ginibre, J., Velo, G. (1979). On a class of nonlinear Schrödinger equations I, II. J. Func. Anal. 32:1-71.
    • (1979) J. Func. Anal. , vol.32 , pp. 1-71
    • Ginibre, J.1    Velo, G.2
  • 12
    • 8744261467 scopus 로고    scopus 로고
    • Preprint
    • Grikurov, V. (1999). Preprint.
    • (1999)
    • Grikurov, V.1
  • 13
    • 0000468151 scopus 로고
    • Stability of solitary waves in presence of symmetry I
    • Grillakis, M., Shatah, J., Strauss, W. (1987). Stability of solitary waves in presence of symmetry I. J. Func. Anal. 74(1):160-197.
    • (1987) J. Func. Anal. , vol.74 , Issue.1 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 14
    • 29444432472 scopus 로고
    • Stability of solitary waves in presence of symmetry II
    • Grillakis, M., Shatah, J., Strauss, W. (1990). Stability of solitary waves in presence of symmetry II. J. Func. Anal. 94(2):308-384.
    • (1990) J. Func. Anal. , vol.94 , Issue.2 , pp. 308-384
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 15
    • 0010967013 scopus 로고
    • Asymptotic completeness for the impact parameter approximation to three particle scattering
    • Hagedorn, G. (1982). Asymptotic completeness for the impact parameter approximation to three particle scattering. Ann. Inst. Henri Poincaré. 36(1): 19-40.
    • (1982) Ann. Inst. Henri Poincaré , vol.36 , Issue.1 , pp. 19-40
    • Hagedorn, G.1
  • 16
    • 84972562665 scopus 로고
    • m), m ≥ 5
    • m), m ≥ 5. Duke Math. J. 47(1):57-80.
    • (1982) Duke Math. J. , vol.47 , Issue.1 , pp. 57-80
    • Jensen, A.1
  • 18
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time decay of the wave functions
    • Jensen, A., Kato, T. (1979). Spectral properties of Schrödinger operators and time decay of the wave functions. Duke Math. J. 46(3):583-611.
    • (1979) Duke Math. J. , vol.46 , Issue.3 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 19
    • 0013378467 scopus 로고
    • Linear differential equations in banach spaces
    • Providence, RI: Amer. Mathematical Society
    • Krein, S. G. (1971). Linear Differential Equations in Banach Spaces. Transl. Math. Mon. 29. Providence, RI: Amer. Mathematical Society.
    • (1971) Transl. Math. Mon. , vol.29
    • Krein, S.G.1
  • 20
    • 0036882736 scopus 로고    scopus 로고
    • Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations
    • Martel, Y. F., Merle, F., Tsai, T.-P. (2001). Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations. Comm. Math. Phys. 231:347-373.
    • (2001) Comm. Math. Phys. , vol.231 , pp. 347-373
    • Martel, Y.F.1    Merle, F.2    Tsai, T.-P.3
  • 22
    • 0037430095 scopus 로고    scopus 로고
    • Dispersion and strichartz estimates for some finite rank perturbations of the laplace operator
    • Nier, F., Soffer, A. (2003). Dispersion and Strichartz estimates for some finite rank perturbations of the Laplace operator. J. Func. Anal. 198(2):511-535.
    • (2003) J. Func. Anal. , vol.198 , Issue.2 , pp. 511-535
    • Nier, F.1    Soffer, A.2
  • 24
    • 3142781631 scopus 로고    scopus 로고
    • Some results on the scattering of weakly interacting solitons for nonlinear Schrödinger equation
    • Demuth et al., M., eds. Spectral Theory, Microlocal Analysis, Singular Manifolds. Berlin: Akademie Verlag
    • Perelman, G. (1997). Some results on the scattering of weakly interacting solitons for nonlinear Schrödinger equation. In: Demuth et al., M., eds. Spectral Theory, Microlocal Analysis, Singular Manifolds. Math. Top. 14. Berlin: Akademie Verlag, pp. 78-137.
    • (1997) Math. Top. , vol.14 , pp. 78-137
    • Perelman, G.1
  • 25
    • 0000301325 scopus 로고
    • Multichannel nonlinear scattering theory for nonintegrable equations I
    • Soffer, A., Weinstein, M. I. (1990). Multichannel nonlinear scattering theory for nonintegrable equations I. Comm. Math. Phys. 133(1):119-146.
    • (1990) Comm. Math. Phys. , vol.133 , Issue.1 , pp. 119-146
    • Soffer, A.1    Weinstein, M.I.2
  • 26
    • 0001641727 scopus 로고
    • Multichannel nonlinear scattering theory for nonintegrable equations II
    • Soffer, A., Weinstein, M. I. (1992). Multichannel nonlinear scattering theory for nonintegrable equations II. J. Diff. Eq. 98(2):376-390.
    • (1992) J. Diff. Eq. , vol.98 , Issue.2 , pp. 376-390
    • Soffer, A.1    Weinstein, M.I.2
  • 27
    • 0003230098 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation. Self-focusing and wave collapse
    • New York: Springer
    • Sulem, C., Sulem, P.-L. (1999). The Nonlinear Schrödinger Equation. Self-focusing and Wave Collapse. Appl. Math. Sciences, 139. New York: Springer.
    • (1999) Appl. Math. Sciences , vol.139
    • Sulem, C.1    Sulem, P.-L.2
  • 28
    • 0036221809 scopus 로고    scopus 로고
    • Asymptotic dynamics of nonlinear Schrödinger equations: Resonance dominated and dispersion dominated solutions
    • Tsai, T.-P., Yau, H.-T. (2002a). Asymptotic dynamics of nonlinear Schrödinger equations: Resonance dominated and dispersion dominated solutions. Comm. Pure Appl. Math. 55:153-216.
    • (2002) Comm. Pure Appl. Math. , vol.55 , pp. 153-216
    • Tsai, T.-P.1    Yau, H.-T.2
  • 29
    • 0036350836 scopus 로고    scopus 로고
    • Relaxation of exited states in nonlinear Schrödinger equations
    • Tsai, T.-P., Yau, H.-T. (2002b). Relaxation of exited states in nonlinear Schrödinger equations. IMRN 31:1629-1673.
    • (2002) IMRN , vol.31 , pp. 1629-1673
    • Tsai, T.-P.1    Yau, H.-T.2
  • 30
    • 0036946822 scopus 로고    scopus 로고
    • Stable directions for exited states of nonlinear Schrödinger equations
    • Tsai, T.-P., Yau, H.-T. (2002c). Stable directions for exited states of nonlinear Schrödinger equations. Comm. PDE 27(11-12):2363-2402.
    • (2002) Comm. PDE , vol.27 , Issue.11-12 , pp. 2363-2402
    • Tsai, T.-P.1    Yau, H.-T.2
  • 31
    • 0038707659 scopus 로고    scopus 로고
    • Classification of a symptotic profiles of nonlinear Schrödinger equations with small initial data
    • Tsai, T.-P., Yau, H.-T. (2002d). Classification of a symptotic profiles of nonlinear Schrödinger equations with small initial data. Adv. Theor. Math. Phys. 6(1):107-139.
    • (2002) Adv. Theor. Math. Phys. , vol.6 , Issue.1 , pp. 107-139
    • Tsai, T.-P.1    Yau, H.-T.2
  • 32
    • 0000686130 scopus 로고
    • Modulation stability of ground states of nonlinear Schrödinger equations
    • Weinstein, M. I. (1985). Modulation stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 16(3):472-491.
    • (1985) SIAM J. Math. Anal. , vol.16 , Issue.3 , pp. 472-491
    • Weinstein, M.I.1
  • 33
    • 84990553584 scopus 로고
    • Lyapunov stability of ground states of nonlinear dispersive evolution equations
    • Weinstein, M. I. (1986). Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math. 39(1):51-68.
    • (1986) Comm. Pure Appl. Math. , vol.39 , Issue.1 , pp. 51-68
    • Weinstein, M.I.1
  • 34
    • 0034349544 scopus 로고    scopus 로고
    • Center manifold for nonintegrable nonliear Schrödinger quations on the line
    • Weder, R. (2000). Center manifold for nonintegrable nonliear Schrödinger quations on the line. Comm. Math. Phys. 215(2):343-356.
    • (2000) Comm. Math. Phys. , vol.215 , Issue.2 , pp. 343-356
    • Weder, R.1
  • 35
    • 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(3):551-581.
    • (1995) J. Math. Soc. Japan , vol.47 , Issue.3 , pp. 551-581
    • Yajima, K.1
  • 36
    • 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(20): 311-346.
    • (1995) J. Math. Sci. Univ. Tokyo , vol.2 , Issue.20 , pp. 311-346
    • Yajima, K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.