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Volumn 15, Issue 1, 2005, Pages

Hierarchy of bifurcations in the truncated and forced nonlinear Schrödinger model

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EID: 17744374347     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1831591     Document Type: Article
Times cited : (21)

References (43)
  • 1
    • 0006044307 scopus 로고    scopus 로고
    • Chaos near resonance
    • Springer, New York
    • G. Haller, Chaos Near Resonance, Applied Mathematical Sciences, Vol. 138 (Springer, New York, 1999).
    • (1999) Applied Mathematical Sciences , vol.138
    • Haller, G.1
  • 2
    • 17744383456 scopus 로고    scopus 로고
    • Westview, Advanced Book Program, Boulder, CO
    • J. Moloney and A. Newell, Nonlinear Optics (Westview, Advanced Book Program, Boulder, CO, 2004).
    • (2004) Nonlinear Optics
    • Moloney, J.1    Newell, A.2
  • 3
    • 46149129941 scopus 로고
    • A quasi-periodic route to chaos in a near-integrable PDE
    • A. Bishop, M. Forest, D. McLaughlin, and E. Overman II, "A quasi-periodic route to chaos in a near-integrable PDE," Physica D 23, 293-328 (1986).
    • (1986) Physica D , vol.23 , pp. 293-328
    • Bishop, A.1    Forest, M.2    McLaughlin, D.3    Overman II, E.4
  • 4
    • 0011368959 scopus 로고
    • Nonlinear dynamics in driven, damped sine-Gordon systems
    • A. R. Bishop and P. S. Lomdahl, "Nonlinear dynamics in driven, damped sine-Gordon systems," Physica D 18, 54-66 (1986); Solitons and Coherent Structures (Santa Barbara, CA, 1985).
    • (1986) Physica D , vol.18 , pp. 54-66
    • Bishop, A.R.1    Lomdahl, P.S.2
  • 5
    • 0011368959 scopus 로고
    • Santa Barbara, CA
    • A. R. Bishop and P. S. Lomdahl, "Nonlinear dynamics in driven, damped sine-Gordon systems," Physica D 18, 54-66 (1986); Solitons and Coherent Structures (Santa Barbara, CA, 1985).
    • (1985) Solitons and Coherent Structures
  • 6
    • 0002647995 scopus 로고
    • A model representation of chaotic attractors for the driven, damped pendulum chain
    • A. Bishop, M. Forest, D. McLaughlin, and E. Overman II, "A model representation of chaotic attractors for the driven, damped pendulum chain," Phys. Lett. A 144, 17-25 (1990).
    • (1990) Phys. Lett. A , vol.144 , pp. 17-25
    • Bishop, A.1    Forest, M.2    McLaughlin, D.3    Overman II, E.4
  • 7
    • 0000593885 scopus 로고
    • Correlations between chaos in a perturbed sine-gordon equation and a truncated model system
    • A. Bishop, R. Flesch, M. Forest, D. McLaughlin, and E. Overman II, "Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system," SIAM J. Math. Anal. 21, 1511-1536 (1990).
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1511-1536
    • Bishop, A.1    Flesch, R.2    Forest, M.3    McLaughlin, D.4    Overman II, E.5
  • 8
    • 0012421465 scopus 로고    scopus 로고
    • The use of manifold tangencies to predict orbits, bifurcations, and estimate escape in driven systems
    • S. Bishop and M. Clifford, "The use of manifold tangencies to predict orbits, bifurcations, and estimate escape in driven systems," Chaos, Solitons Fractals 7, 1537-1553 (1996).
    • (1996) Chaos, Solitons Fractals , vol.7 , pp. 1537-1553
    • Bishop, S.1    Clifford, M.2
  • 9
    • 45549115374 scopus 로고
    • Quasi-periodic route to chaos in a near-integrable PDE: Homoclinic crossings
    • A. Bishop, D. McLaughlin, M. Forest, and E. I. Overman, "Quasi-periodic route to chaos in a near-integrable PDE: Homoclinic crossings," Phys. Lett. A 127, 335-340 (1988).
    • (1988) Phys. Lett. A , vol.127 , pp. 335-340
    • Bishop, A.1    McLaughlin, D.2    Forest, M.3    Overman, E.I.4
  • 11
    • 0242376125 scopus 로고    scopus 로고
    • The nonlinear Schrödinger equation as both a PDE and a dynamical system
    • North-Holland, Amsterdam
    • D. Cai, D. W. McLaughlin, and K. T. R. McLaughlin, "The nonlinear Schrödinger equation as both a PDE and a dynamical system," in Handbook of Dynamical Systems (North-Holland, Amsterdam, 2002), Vol. 2, pp. 599-675.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 599-675
    • Cai, D.1    McLaughlin, D.W.2    McLaughlin, K.T.R.3
  • 12
    • 0039533869 scopus 로고
    • Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems
    • G. Kovacic, "Singular perturbation theory for homoclinic orbits in a class of near-integrable dissipative systems," J. Dyn. Differ. Equ. 5, 559-597 (1993).
    • (1993) J. Dyn. Differ. Equ. , vol.5 , pp. 559-597
    • Kovacic, G.1
  • 13
    • 4243593317 scopus 로고
    • Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation
    • G. Haller and S. Wiggins, "Multi-pulse jumping orbits and homoclinic trees in a modal truncation of the damped-forced nonlinear Schrödinger equation," Physica D 85, 311-347 (1995).
    • (1995) Physica D , vol.85 , pp. 311-347
    • Haller, G.1    Wiggins, S.2
  • 14
    • 21844501994 scopus 로고
    • N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
    • Communicated by P. Holmes
    • G. Haller and S. Wiggins, "N-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems," Arch. Ration. Mech. Anal. 130, 25-101 (1995). Communicated by P. Holmes.
    • (1995) Arch. Ration. Mech. Anal. , vol.130 , pp. 25-101
    • Haller, G.1    Wiggins, S.2
  • 15
    • 0002307231 scopus 로고
    • Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
    • G. Kovacic and S. Wiggins, "Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation," Physica D 57, 185-225 (1992).
    • (1992) Physica D , vol.57 , pp. 185-225
    • Kovacic, G.1    Wiggins, S.2
  • 16
    • 0012078988 scopus 로고    scopus 로고
    • Homoclinic orbits for PDE's
    • Recent Advances in Partial Differential Equations, Venice 1996, American Mathematic Society, Providence, RI
    • D. W. McLaughlin and J. Shatah, "Homoclinic orbits for PDE's," in Recent Advances in Partial Differential Equations, Venice 1996, Proc. Sym pos. Appl. Math., Vol. 54 (American Mathematic Society, Providence, RI, 1998), pp. 281-299.
    • (1998) Proc. Sym Pos. Appl. Math. , vol.54 , pp. 281-299
    • McLaughlin, D.W.1    Shatah, J.2
  • 17
    • 0242276354 scopus 로고    scopus 로고
    • Orbits homoclinic to centre manifolds of conservative PDEs
    • J. Shatah and C. Zeng, "Orbits homoclinic to centre manifolds of conservative PDEs," Nonlinearity 16, 591-614 (2003).
    • (2003) Nonlinearity , vol.16 , pp. 591-614
    • Shatah, J.1    Zeng, C.2
  • 18
    • 0042384685 scopus 로고    scopus 로고
    • Resonant tori and instabilities in Hamiltonian systems
    • A. Litvak-Hinenzon and V. Rom-Kedar, "Resonant tori and instabilities in Hamiltonian systems," Nonlinearity 15, 1149-1177 (2002).
    • (2002) Nonlinearity , vol.15 , pp. 1149-1177
    • Litvak-Hinenzon, A.1    Rom-Kedar, V.2
  • 19
    • 34250119129 scopus 로고
    • Algebraic decay in self-similar Markov chains
    • J. Hanson, J. Cary, and J. Meiss, "Algebraic decay in self-similar Markov chains," J. Stat. Phys. 39, 27-345 (1985).
    • (1985) J. Stat. Phys. , vol.39 , pp. 27-345
    • Hanson, J.1    Cary, J.2    Meiss, J.3
  • 20
    • 0036887936 scopus 로고    scopus 로고
    • Chaos, fractional kinetics, and anomalous transport
    • G. M. Zaslavsky, "Chaos, fractional kinetics, and anomalous transport," Phys. Rep. 371, 461-580 (2002).
    • (2002) Phys. Rep. , vol.371 , pp. 461-580
    • Zaslavsky, G.M.1
  • 21
    • 0010890055 scopus 로고
    • Symplectic maps, variational principles, and transport
    • J. Meiss, "Symplectic maps, variational principles, and transport," Rev. Mod. Phys. 64, 795-848 (1992).
    • (1992) Rev. Mod. Phys. , vol.64 , pp. 795-848
    • Meiss, J.1
  • 22
    • 10044277502 scopus 로고
    • Homoclinic tangles - Classification and applications
    • V. Rom-Kedar, "Homoclinic tangles - classification and applications," Nonlinearity 7, 441-473 (1994).
    • (1994) Nonlinearity , vol.7 , pp. 441-473
    • Rom-Kedar, V.1
  • 23
    • 84908024292 scopus 로고
    • An exponential estimate of the time of stability of near-integrable Hamiltonian systems
    • N. Nekhoroshev, "An exponential estimate of the time of stability of near-integrable Hamiltonian systems," Russ. Math. Surveys 32, 1-65 (1977).
    • (1977) Russ. Math. Surveys , vol.32 , pp. 1-65
    • Nekhoroshev, N.1
  • 24
    • 0000163515 scopus 로고
    • Effective stability for Hamiltonian systems near an elliptic point, with an application to the restricted three-body problem
    • A. Giorgilli, A. Delshams, E. Fontich, L. Galgani, and C. Simó, "Effective stability for Hamiltonian systems near an elliptic point, with an application to the restricted three-body problem," J. Diff. Eqns. 77, 167 (1989).
    • (1989) J. Diff. Eqns. , vol.77 , pp. 167
    • Giorgilli, A.1    Delshams, A.2    Fontich, E.3    Galgani, L.4    Simó, C.5
  • 25
    • 22244441450 scopus 로고
    • Topology and mechanics. I
    • S. Smale, "Topology and mechanics. I," Invent Math. 10, 305-331 (1970).
    • (1970) Invent Math. , vol.10 , pp. 305-331
    • Smale, S.1
  • 26
    • 0003365533 scopus 로고    scopus 로고
    • Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, [Translated from the Russian manuscript by A. Kononenko and A. Semenovich.]
    • L. M. Lerman and Y. L. Umanskiy, Four-dimensional Integrable Hamiltonian Systems with Simple Singular Points (Topological Aspects), Translations of Mathematical Monographs, Vol. 176 (American Mathematical Society, Providence, RI, 1998). [Translated from the Russian manuscript by A. Kononenko and A. Semenovich.]
    • (1998) Four-dimensional Integrable Hamiltonian Systems with Simple Singular Points (Topological Aspects) , vol.176
    • Lerman, L.M.1    Umanskiy, Y.L.2
  • 27
    • 0004282301 scopus 로고
    • Benjamin/ Cummings, Advanced Book Program, Reading, MA, Second edition, revised and enlarged, with the assistance of T. Ratiu and R. Cushman
    • R. Abraham and J. E. Marsden, Foundations of Mechanics (Benjamin/ Cummings, Advanced Book Program, Reading, MA, 1978). Second edition, revised and enlarged, with the assistance of T. Ratiu and R. Cushman.
    • (1978) Foundations of Mechanics
    • Abraham, R.1    Marsden, J.E.2
  • 28
    • 0004029931 scopus 로고
    • Encyclopedia of Mathematical Sciences 2nd ed. Springer, Berlin
    • V. I. Arnol'd, Dynamical Systems III, Encyclopedia of Mathematical Sciences Vol. 3, 2nd ed. (Springer, Berlin, 1993).
    • (1993) Dynamical Systems III , vol.3
    • Arnol'd, V.I.1
  • 30
    • 0000939872 scopus 로고
    • Advances in Soviet Mathematics, edited by A. T. Fomenko (American Mathematical Society, Providence, RI) [Translated from the Russian.]
    • Topological Classification of Integrable Systems, Advances in Soviet Mathematics, Vol. 6, edited by A. T. Fomenko (American Mathematical Society, Providence, RI, 1991). [Translated from the Russian.]
    • (1991) Topological Classification of Integrable Systems , vol.6
  • 32
    • 0001470585 scopus 로고
    • Methods of calculation of the Fomenko-Zieschang invariant
    • Topological Classification of Integrable Systems, American Mathematical Society, Providence, RI
    • A. V. Bolsinov, "Methods of calculation of the Fomenko-Zieschang invariant," in Topological Classification of Integrable Systems, Adv. Soviet Math, Vol. 6 (American Mathematical Society, Providence, RI, 1991), pp. 147-183.
    • (1991) Adv. Soviet Math , vol.6 , pp. 147-183
    • Bolsinov, A.V.1
  • 33
    • 0037089436 scopus 로고    scopus 로고
    • Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems
    • A. Litvak-Hinenzon and V. Rom-Kedar, "Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems," Physica D 164, 213-250 (2002).
    • (2002) Physica D , vol.164 , pp. 213-250
    • Litvak-Hinenzon, A.1    Rom-Kedar, V.2
  • 35
    • 0000288001 scopus 로고    scopus 로고
    • Chaotic Hamiltonian dynamics of particle's horizontal motion in the atmosphere
    • V. Rom-Kedar, Y. Dvorkin, and N. Paldor, "Chaotic Hamiltonian dynamics of particle's horizontal motion in the atmosphere," Physica D 106, 389-431 (1997).
    • (1997) Physica D , vol.106 , pp. 389-431
    • Rom-Kedar, V.1    Dvorkin, Y.2    Paldor, N.3
  • 36
    • 21744443351 scopus 로고    scopus 로고
    • Parabolic resonances and instabilities
    • V. Rom-Kedar, "Parabolic resonances and instabilities," Chaos 7, 148-158 (1997).
    • (1997) Chaos , vol.7 , pp. 148-158
    • Rom-Kedar, V.1
  • 37
    • 0000585760 scopus 로고
    • Dynamics bifurcation in Hamiltonian systems with one degree of freedom
    • N. Lebovitz and A. Pesci, "Dynamics bifurcation in Hamiltonian systems with one degree of freedom," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 55, 1117-1133 (1995).
    • (1995) SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. , vol.55 , pp. 1117-1133
    • Lebovitz, N.1    Pesci, A.2
  • 38
    • 0000234399 scopus 로고
    • Action-angle variables, and their generalizations
    • N. N. Nehorošev, "Action-angle variables, and their generalizations," Trans. Mosc. Math. Soc. 26, 181-198 (1972).
    • (1972) Trans. Mosc. Math. Soc. , vol.26 , pp. 181-198
    • Nehorošev, N.N.1
  • 40
    • 0012910628 scopus 로고    scopus 로고
    • Remarks on the definition of hyperbolic tori of Hamiltonian systems
    • S. V. Bolotin and D. V. Treschev, "Remarks on the definition of hyperbolic tori of Hamiltonian systems," Regular Chaotic Dyn. 5, 401-412 (2000).
    • (2000) Regular Chaotic Dyn. , vol.5 , pp. 401-412
    • Bolotin, S.V.1    Treschev, D.V.2
  • 41
    • 0000882204 scopus 로고
    • On elliptic lower dimensional tori in Hamiltonian systems
    • J. Pöschel, "On elliptic lower dimensional tori in Hamiltonian systems," Math. Z. 202, 559-608 (1989).
    • (1989) Math. Z. , vol.202 , pp. 559-608
    • Pöschel, J.1
  • 43
    • 0042397481 scopus 로고
    • Passage through a separatrix in a resonance problem with a slowly varying parameter
    • A. I. Neishtadt, "Passage through a separatrix in a resonance problem with a slowly varying parameter," Prikl. Mat. Mekh. 39, 1331-1334 (1975).
    • (1975) Prikl. Mat. Mekh. , vol.39 , pp. 1331-1334
    • Neishtadt, A.I.1


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