메뉴 건너뛰기




Volumn 53, Issue 10, 2000, Pages 1222-1283

Homoclinic orbits for a perturbed nonlinear Schrödinger equation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0034378439     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0312(200010)53:10<1222::AID-CPA2>3.0.CO;2-F     Document Type: Article
Times cited : (21)

References (38)
  • 1
    • 33748109655 scopus 로고    scopus 로고
    • Existence and persistence of invariant manifolds for semiflows in Banach space
    • Bates, P. W.; Lu, K.; Zeng, C. Existence and persistence of invariant manifolds for semiflows in Banach space. Mem. Amer. Math. Soc. 135 (1998), no. 645.
    • (1998) Mem. Amer. Math. Soc. , vol.135 , pp. 645
    • Bates, P.W.1    Lu, K.2    Zeng, C.3
  • 2
    • 0033409820 scopus 로고    scopus 로고
    • Persistence of overflowing manifolds for semiflow
    • Bates, P. W.; Lu, K.; Zeng, C. Persistence of overflowing manifolds for semiflow. Comm. Pure Appl. Math. 52 (1999), no. 8, 983-1046.
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.8 , pp. 983-1046
    • Bates, P.W.1    Lu, K.2    Zeng, C.3
  • 3
    • 85037770342 scopus 로고    scopus 로고
    • Invariant foliations near normally hyperbolic invariant manifolds for semiflows
    • in press
    • Bates, P. W.; Lu, K.; Zeng, C. Invariant foliations near normally hyperbolic invariant manifolds for semiflows. Trans. Amer. Math. Soc., in press.
    • Trans. Amer. Math. Soc.
    • Bates, P.W.1    Lu, K.2    Zeng, C.3
  • 4
    • 0003197180 scopus 로고    scopus 로고
    • An introduction to nonlinear Schrödinger equations
    • Instituto de Matemática Universidade Federal do Rio de Janeiro, Rio de Janeiro
    • Cazenave, T. An introduction to nonlinear Schrödinger equations. Textos de Métodos Matemáticos No. 22, Instituto de Matemática Universidade Federal do Rio de Janeiro, Rio de Janeiro, 1996.
    • (1996) Textos de Métodos Matemáticos , vol.22
    • Cazenave, T.1
  • 10
    • 0001522381 scopus 로고
    • Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation
    • Ercolani, N.; Forest, M. G.; McLaughlin, D. W. Geometry of the modulational instability. III. Homoclinic orbits for the periodic sine-Gordon equation. Phys. D 43 (1990), no. 2-3, 349-384.
    • (1990) Phys. D , vol.43 , Issue.2-3 , pp. 349-384
    • Ercolani, N.1    Forest, M.G.2    McLaughlin, D.W.3
  • 11
    • 0012721796 scopus 로고
    • Toward a topological classification of integrable PDEs
    • The geometry of Hamiltonian systems (Berkeley, CA, 1989), Springer, New York
    • Ercolani, N. M.; McLaughlin, D. W. Toward a topological classification of integrable PDEs. The geometry of Hamiltonian systems (Berkeley, CA, 1989), 111-129. Math. Sci. Res. Inst. Publ., 22. Springer, New York, 1991.
    • (1991) Math. Sci. Res. Inst. Publ. , vol.22 , pp. 111-129
    • Ercolani, N.M.1    McLaughlin, D.W.2
  • 12
    • 0003285244 scopus 로고
    • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
    • Springer, New York-Berlin
    • Guckenheimer, J.; Holmes, P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Applied Mathematical Sciences, 42. Springer, New York-Berlin, 1983.
    • (1983) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 13
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • American Mathematical Society, Providence, R.I.
    • Hale, Jack K. Asymptotic behavior of dissipative systems. Mathematical Surveys and Monographs, 25. American Mathematical Society, Providence, R.I., 1988.
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 14
    • 0032394910 scopus 로고    scopus 로고
    • Multi-dimensional homoclinic jumping and the discretized NLS equation
    • Haller, G. Multi-dimensional homoclinic jumping and the discretized NLS equation. Comm. Math. Phys. 193 (1998), no. 1, 1-46.
    • (1998) Comm. Math. Phys. , vol.193 , Issue.1 , pp. 1-46
    • Haller, G.1
  • 15
    • 0012078987 scopus 로고    scopus 로고
    • Homoclinic jumping in the perturbed nonlinear Schrödinger equation
    • Haller, G. Homoclinic jumping in the perturbed nonlinear Schrödinger equation. Comm. Pure Appl. Math. 52 (1999), no. 1, 1-47.
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.1 , pp. 1-47
    • Haller, G.1
  • 16
    • 0008495183 scopus 로고
    • Orbits homoclinic to resonances: The Hamiltonian case
    • Haller, G.; Wiggins, S. Orbits homoclinic to resonances: the Hamiltonian case. Phys. D 66 (1993), no. 3-4, 298-346.
    • (1993) Phys. D , vol.66 , Issue.3-4 , pp. 298-346
    • Haller, G.1    Wiggins, S.2
  • 17
    • 0019666924 scopus 로고
    • A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
    • Holmes, P.; Marsden, J. A partial differential equation with infinitely many periodic orbits: chaotic oscillations of a forced beam. Arch. Rational Mech. Anal. 76 (1981), no. 2, 135-165.
    • (1981) Arch. Rational Mech. Anal. , vol.76 , Issue.2 , pp. 135-165
    • Holmes, P.1    Marsden, J.2
  • 19
    • 21844500253 scopus 로고
    • Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems
    • Kovačič, G. Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems. SIAM J. Math. Anal. 26 (1995), no. 6, 1611-1643.
    • (1995) SIAM J. Math. Anal. , vol.26 , Issue.6 , pp. 1611-1643
    • Kovačič, G.1
  • 20
    • 0002307231 scopus 로고
    • Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
    • Kovačič, G.; Wiggins, S. Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation. Phys. D 57 (1992), no. 1-2, 185-225.
    • (1992) Phys. D , vol.57 , Issue.1-2 , pp. 185-225
    • Kovačič, G.1    Wiggins, S.2
  • 21
    • 0009071415 scopus 로고    scopus 로고
    • Invariant manifolds and fibrations for perturbed nonlinear schrödinger equations
    • Springer, New York
    • Li, C.; Wiggins, S. Invariant manifolds and fibrations for perturbed nonlinear Schrödinger equations. Applied Mathematical Sciences, 128. Springer, New York, 1997.
    • (1997) Applied Mathematical Sciences , vol.128
    • Li, C.1    Wiggins, S.2
  • 22
    • 0040727879 scopus 로고
    • Doctoral dissertation, Princeton University
    • Li, Y. Chaotic Behavior in PDEs. Doctoral dissertation, Princeton University, 1993.
    • (1993) Chaotic Behavior in PDEs
    • Li, Y.1
  • 23
    • 0000590755 scopus 로고    scopus 로고
    • Smale horseshoes and symbolic dynamics in perturbed nonlinear Schrödinger equations
    • Li, Y. Smale horseshoes and symbolic dynamics in perturbed nonlinear Schrödinger equations. J. Nonlinear Sci. 9 (1999), no. 4, 363-415.
    • (1999) J. Nonlinear Sci. , vol.9 , Issue.4 , pp. 363-415
    • Li, Y.1
  • 24
    • 34249767027 scopus 로고
    • Morse and Mel'nikov functions for NLS PDEs
    • Li, Y.; McLaughlin, D. W. Morse and Mel'nikov functions for NLS PDEs. Comm. Math. Phys. 162 (1994), no. 1, 175-214.
    • (1994) Comm. Math. Phys. , vol.162 , Issue.1 , pp. 175-214
    • Li, Y.1    McLaughlin, D.W.2
  • 25
    • 0000038726 scopus 로고    scopus 로고
    • Homoclinic orbits and chaos in discretized perturbed NLS systems. I. Homoclinic orbits
    • Li, Y.; McLaughlin, D. W. Homoclinic orbits and chaos in discretized perturbed NLS systems. I. Homoclinic orbits. J. Nonlinear Sci. 7 (1997), no. 3, 211-269.
    • (1997) J. Nonlinear Sci. , vol.7 , Issue.3 , pp. 211-269
    • Li, Y.1    McLaughlin, D.W.2
  • 26
    • 0030506927 scopus 로고    scopus 로고
    • Persistent homoclinic orbits for a perturbed nonlinear Schrödinger equation
    • Li, Y.; McLaughlin, D. W.; Shatah, J.; Wiggins, S. Persistent homoclinic orbits for a perturbed nonlinear Schrödinger equation. Comm. Pure Appl. Math. 49 (1996), no. 11, 1175-1255.
    • (1996) Comm. Pure Appl. Math. , vol.49 , Issue.11 , pp. 1175-1255
    • Li, Y.1    McLaughlin, D.W.2    Shatah, J.3    Wiggins, S.4
  • 27
    • 0041716979 scopus 로고    scopus 로고
    • Homoclinic orbits and chaos in discretized perturbed NLS systems. II. Symbolic dynamics
    • Li, Y.; Wiggins, S. Homoclinic orbits and chaos in discretized perturbed NLS systems. II. Symbolic dynamics. J. Nonlinear Sci. 7 (1997), no. 4, 315-370.
    • (1997) J. Nonlinear Sci. , vol.7 , Issue.4 , pp. 315-370
    • Li, Y.1    Wiggins, S.2
  • 28
    • 0002822575 scopus 로고    scopus 로고
    • Homoclinic bifurcations with weakly expanding center manifolds
    • Dynamics reported, Springer, Berlin
    • Lin, X.-B. Homoclinic bifurcations with weakly expanding center manifolds. Dynamics reported, 99-189. Dynam. Report. Expositions Dynam. Systems (N.S.), 5. Springer, Berlin, 1996.
    • (1996) Dynam. Report. Expositions Dynam. Systems (N.S.) , vol.5 , pp. 99-189
    • Lin, X.-B.1
  • 29
    • 0041716982 scopus 로고
    • Whiskered tori for NLS equations
    • Important developments in soliton theory
    • McLaughlin, D. W. Whiskered tori for NLS equations. Important developments in soliton theory, 537-558. Springer Ser. Nonlinear Dynam. Springer, Berlin, 1993.
    • (1993) Springer Ser. Nonlinear Dynam. Springer, Berlin , pp. 537-558
    • McLaughlin, D.W.1
  • 30
    • 0002063004 scopus 로고
    • Whiskered tori for integrable PDEs: Chaotic behavior in near integrable pde's
    • Surveys in applied mathematics, Vol. 1, Plenum, New York
    • McLaughlin, D. W.; Overman, E. A. Whiskered tori for integrable PDEs: chaotic behavior in near integrable pde's. Surveys in applied mathematics, Vol. 1, 83-203. Surveys Appl. Math., 1. Plenum, New York, 1995.
    • (1995) Surveys Appl. Math. , vol.1 , pp. 83-203
    • McLaughlin, D.W.1    Overman, E.A.2
  • 31
    • 0000038096 scopus 로고    scopus 로고
    • Homoclinic orbits in a four-dimensional model of a perturbed NLS equation: A geometric singular perturbation study
    • Dynamics reported, Springer, Berlin
    • McLaughlin, D. W.; Overman, E. A., II; Wiggins, S.; Xiong, C. Homoclinic orbits in a four-dimensional model of a perturbed NLS equation: a geometric singular perturbation study. Dynamics reported, 190-287. Dynam. Report. Expositions Dynam. Systems (N.S.), 5. Springer, Berlin, 1996.
    • (1996) Dynam. Report. Expositions Dynam. Systems (N.S.) , vol.5 , pp. 190-287
    • McLaughlin, D.W.1    Overman E.A. II2    Wiggins, S.3    Xiong, C.4
  • 32
    • 0012078988 scopus 로고    scopus 로고
    • Homoclinic orbits for PDE's
    • Recent advances in partial differential equations, Venice 1996, Amer. Math. Soc., Providence, R.I.
    • McLaughlin, D. W.; Shatah, J. Homoclinic orbits for PDE's. Recent advances in partial differential equations, Venice 1996, 281-299. Proc. Sympos. Appl. Math., 54. Amer. Math. Soc., Providence, R.I., 1998.
    • (1998) Proc. Sympos. Appl. Math. , vol.54 , pp. 281-299
    • McLaughlin, D.W.1    Shatah, J.2
  • 33
    • 0040787052 scopus 로고
    • Stable and random motions in dynamical systems. With special emphasis on celestial mechanics
    • Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N.J. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo
    • Moser, J. Stable and random motions in dynamical systems. With special emphasis on celestial mechanics. Hermann Weyl Lectures, the Institute for Advanced Study, Princeton, N.J. Annals of Mathematics Studies, No. 77. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1973.
    • (1973) Annals of Mathematics Studies , vol.77
    • Moser, J.1
  • 35
    • 0034406879 scopus 로고    scopus 로고
    • Homoclinic orbits for the perturbed sine-Gordon equation
    • Shatah, J.; Zeng, C. Homoclinic orbits for the perturbed sine-Gordon equation. Comm. Pure Appl. Math. 53 (2000), no. 3, 283-299.
    • (2000) Comm. Pure Appl. Math. , vol.53 , Issue.3 , pp. 283-299
    • Shatah, J.1    Zeng, C.2
  • 37
    • 0003278399 scopus 로고
    • Infinite-dimensional dynamical systems in mechanics and physics
    • Springer, New York-Berlin
    • Temam, R. Infinite-dimensional dynamical systems in mechanics and physics. Applied Mathematical Sciences, 68. Springer, New York-Berlin, 1988.
    • (1988) Applied Mathematical Sciences , vol.68
    • Temam, R.1
  • 38
    • 0003272505 scopus 로고
    • Global bifurcations and chaos. Analytical methods
    • Springer, New York-Berlin
    • Wiggins, S. Global bifurcations and chaos. Analytical methods. Applied Mathematical Sciences, 73. Springer, New York-Berlin, 1988.
    • (1988) Applied Mathematical Sciences , vol.73
    • Wiggins, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.