메뉴 건너뛰기




Volumn 124, Issue 1-3, 1998, Pages 137-165

Structural stability of non-ground state traveling waves of coupled nonlinear Schrödinger equations

Author keywords

Hamiltonian perturbation; Liapunov Schmidt reduction; Non ground states; Structural stability; Traveling waves

Indexed keywords


EID: 11544364689     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00184-5     Document Type: Article
Times cited : (30)

References (38)
  • 2
    • 0029270874 scopus 로고
    • Phase-locked stationary solitions states in birefringent nonlinear optical fibers
    • N. Akhmediev, A. Buryak, J. Soto-Crespo, D. Anderson, Phase-locked stationary solitions states in birefringent nonlinear optical fibers, J. Opt. Soc. Am. B 12 (1995) 434-439.
    • (1995) J. Opt. Soc. Am. B , vol.12 , pp. 434-439
    • Akhmediev, N.1    Buryak, A.2    Soto-Crespo, J.3    Anderson, D.4
  • 3
    • 0002085123 scopus 로고
    • Steady state pulses in a birefringent nonlinear optical fiber: Soliton multiplication processes
    • N. Akhmendiev, V. Eleonskii, E. Kulagin, L. Shilnikov, Steady state pulses in a birefringent nonlinear optical fiber: soliton multiplication processes, Sov. Tech. Phys. Lett. 15 (1989) 587-588.
    • (1989) Sov. Tech. Phys. Lett. , vol.15 , pp. 587-588
    • Akhmendiev, N.1    Eleonskii, V.2    Kulagin, E.3    Shilnikov, L.4
  • 4
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • J.C. Alexander, R.A. Gardner, C.K.R.T. Jones, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math. 410 (1990) 167-212.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.C.1    Gardner, R.A.2    Jones, C.K.R.T.3
  • 6
    • 0023150231 scopus 로고
    • Polarization instabilities for solitons in birefringent fibers
    • K.J. Blow, N.J. Doran, D. Wood, Polarization instabilities for solitons in birefringent fibers. Opt. Lett. 12 (3) (1987) 202-204.
    • (1987) Opt. Lett. , vol.12 , Issue.3 , pp. 202-204
    • Blow, K.J.1    Doran, N.J.2    Wood, D.3
  • 7
    • 84975565210 scopus 로고
    • Vector solitons in birefringent nonlinear dispersive media
    • D.N. Christodoulides, R.I. Joseph, Vector solitons in birefringent nonlinear dispersive media. Opt. Lett. 13 (1) (1988) 53-55.
    • (1988) Opt. Lett. , vol.13 , Issue.1 , pp. 53-55
    • Christodoulides, D.N.1    Joseph, R.I.2
  • 10
    • 0038659316 scopus 로고
    • An oscillation method for fourth-order, self-adjoint, two-point boundary value problems with nonlinear eigenvalues
    • L. Greenberg, An oscillation method for fourth-order, self-adjoint, two-point boundary value problems with nonlinear eigenvalues, SIAM J. Math. Anal. 22 (1991) 1021-1042.
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1021-1042
    • Greenberg, L.1
  • 11
    • 84990623184 scopus 로고
    • Linearized instability for nonlinear Schrödinger and Klein-Gordon equations
    • M. Grillakis, Linearized instability for nonlinear Schrödinger and Klein-Gordon equations, Comm. Pure Appl. Math. XLI (1988) 747-774.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 747-774
    • Grillakis, M.1
  • 12
    • 84990563336 scopus 로고
    • Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system
    • M. Grillakis, Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system, Comm. Pure Appl. Math. XLIII (1990) 299-333.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 299-333
    • Grillakis, M.1
  • 13
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry, I
    • M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry, I, J. Func. Anal. 74 (1987) 160-197.
    • (1987) J. Func. Anal. , vol.74 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 14
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry, II
    • M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry, II, J. Func. Anal. 94 (1990) 308-348.
    • (1990) J. Func. Anal. , vol.94 , pp. 308-348
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 16
    • 0000670781 scopus 로고
    • Instability of standing waves for nonlinear Schrödinger type equations
    • C.R.T. Jones, Instability of standing waves for nonlinear Schrödinger type equations, Ergodic Theory Dynamical Systems 8 (1988) 119-138.
    • (1988) Ergodic Theory Dynamical Systems , vol.8 , pp. 119-138
    • Jones, C.R.T.1
  • 17
    • 0001127339 scopus 로고
    • Second-order perturbations for solitons in optical fibers
    • D. Kaup, Second-order perturbations for solitons in optical fibers, Phys. Rev. A 44 (1991) 4582-4590.
    • (1991) Phys. Rev. A , vol.44 , pp. 4582-4590
    • Kaup, D.1
  • 19
    • 0000452782 scopus 로고
    • Soliton trapping and daughter waves in the Manakov model
    • D. Kaup, B.A. Malomed, Soliton trapping and daughter waves in the Manakov model, Phys. Rev. A 48 (1993) 599-604.
    • (1993) Phys. Rev. A , vol.48 , pp. 599-604
    • Kaup, D.1    Malomed, B.A.2
  • 20
    • 0000127687 scopus 로고
    • Self focusing of optical beams
    • P. Kelley, Self focusing of optical beams, Phys. Rev. Lett. 15 (1965) 1005-1008.
    • (1965) Phys. Rev. Lett. , vol.15 , pp. 1005-1008
    • Kelley, P.1
  • 22
    • 0000732670 scopus 로고
    • Reflectionless transmission through dielectrics and scattering potentials
    • J. Kay, H.E. Moses, Reflectionless transmission through dielectrics and scattering potentials, J. Appl. Phys. 27 12 (1956) 1503-1508.
    • (1956) J. Appl. Phys. 27 , vol.12 , pp. 1503-1508
    • Kay, J.1    Moses, H.E.2
  • 24
    • 84990616663 scopus 로고
    • On the stability of KdV multi-solitons
    • J. Maddocks, R. Sachs, On the stability of KdV multi-solitons, Comm. Pure. Appl. Math. 46 (1993) 867-901.
    • (1993) Comm. Pure. Appl. Math. , vol.46 , pp. 867-901
    • Maddocks, J.1    Sachs, R.2
  • 25
    • 0000763166 scopus 로고
    • On the theory of two-dimensional stationary self-focusing of electromagnetic waves
    • S.V. Manakov, On the theory of two-dimensional stationary self-focusing of electromagnetic waves, JETP 38 (2) (1974) 248-253.
    • (1974) JETP , vol.38 , Issue.2 , pp. 248-253
    • Manakov, S.V.1
  • 26
    • 84975605130 scopus 로고
    • Stability of solitons in birefringent optical fibers, I. Equal propagation amplitudes
    • C. Menyuk, Stability of solitons in birefringent optical fibers, I. Equal propagation amplitudes, Opt. Lett. 12 (1987) 614-616.
    • (1987) Opt. Lett. , vol.12 , pp. 614-616
    • Menyuk, C.1
  • 27
    • 0024914687 scopus 로고
    • Pulse propagation in an elliptically birefringent optical Kerr medium
    • C. Menyuk, Pulse propagation in an elliptically birefringent optical Kerr medium, IEEE J. Qunat. Electron. QE-25 (1989) 2674-2682.
    • (1989) IEEE J. Qunat. Electron. , vol.QE-25 , pp. 2674-2682
    • Menyuk, C.1
  • 28
    • 0002106841 scopus 로고
    • Hamiltonian dynamics of solitons in optical fibers
    • D.J. Muraki, W.L. Kath, Hamiltonian dynamics of solitons in optical fibers, Physica D 48 (1991) 53-64.
    • (1991) Physica D , vol.48 , pp. 53-64
    • Muraki, D.J.1    Kath, W.L.2
  • 29
    • 0000301402 scopus 로고
    • Soliton solutions of multicomponent nonlinear Schrödinger equation
    • Y. Nogami, C.S. Warke, Soliton solutions of multicomponent nonlinear Schrödinger equation, Phys. Lett. A 59 (4) (1976) 251-253.
    • (1976) Phys. Lett. A , vol.59 , Issue.4 , pp. 251-253
    • Nogami, Y.1    Warke, C.S.2
  • 34
    • 35949010580 scopus 로고
    • Bound solitary waves in birefringent optical fiber
    • M.W. Tratnik, J.E. Sipe, Bound solitary waves in birefringent optical fiber, Phys. Rev. A 38 (1988) 2011-2017.
    • (1988) Phys. Rev. A , vol.38 , pp. 2011-2017
    • Tratnik, M.W.1    Sipe, J.E.2
  • 35
    • 0001076665 scopus 로고
    • Dynamics of optical pulses in randomly birefringent fibers
    • T. Ueda, W. Kath, Dynamics of optical pulses in randomly birefringent fibers, Physica D 55 (1992) 166-181.
    • (1992) Physica D , vol.55 , pp. 166-181
    • Ueda, T.1    Kath, W.2
  • 36
    • 0030083457 scopus 로고    scopus 로고
    • Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence
    • P.A. Wai, C.R. Menyuk, Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence, J. Lightwave Tech. 14 (1996) 148-157.
    • (1996) J. Lightwave Tech. , vol.14 , pp. 148-157
    • Wai, P.A.1    Menyuk, C.R.2
  • 37
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • M. Weinstein, Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal 16 (1985) 472-491.
    • (1985) SIAM J. Math. Anal , vol.16 , pp. 472-491
    • Weinstein, M.1
  • 38
    • 84990553584 scopus 로고
    • Liapunov stability of ground states of nonlinear dispersive evolution equations
    • M. Weinstein, Liapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39 (1986) 51-68.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 51-68
    • Weinstein, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.