메뉴 건너뛰기




Volumn 237, Issue 20, 2008, Pages 2649-2671

On the spectra of periodic waves for infinite-dimensional Hamiltonian systems

Author keywords

Hamiltonian systems; Periodic waves; Stability

Indexed keywords

CONTROL NONLINEARITIES; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; INVERSE PROBLEMS; KORTEWEG-DE VRIES EQUATION; LINEARIZATION; NONLINEAR EQUATIONS;

EID: 51249105765     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.03.050     Document Type: Article
Times cited : (134)

References (30)
  • 1
    • 0028060706 scopus 로고
    • Stability theory for periodic pulse train solutions of the nonlinear Schrödinger equation
    • Arnold J. Stability theory for periodic pulse train solutions of the nonlinear Schrödinger equation. IMA J. Appl. Math. 52 (1994) 123-140
    • (1994) IMA J. Appl. Math. , vol.52 , pp. 123-140
    • Arnold, J.1
  • 2
    • 33846325439 scopus 로고    scopus 로고
    • Modulational instability for nonlinear Schrödinger equations with a periodic potential
    • Bronski J., and Rapti Z. Modulational instability for nonlinear Schrödinger equations with a periodic potential. Dyn. Partial Differ. Equ. 2 4 (2005) 335-355
    • (2005) Dyn. Partial Differ. Equ. , vol.2 , Issue.4 , pp. 335-355
    • Bronski, J.1    Rapti, Z.2
  • 4
    • 0035509442 scopus 로고    scopus 로고
    • Stability of repulsive Bose-Einstein condensates in a periodic potential
    • Bronski J., Carr L., Deconinck B., Kutz J., and Promislow K. Stability of repulsive Bose-Einstein condensates in a periodic potential. Phys. Rev. E 63 036612 (2001)
    • (2001) Phys. Rev. E , vol.63 , Issue.036612
    • Bronski, J.1    Carr, L.2    Deconinck, B.3    Kutz, J.4    Promislow, K.5
  • 5
    • 33847169349 scopus 로고    scopus 로고
    • SpectrUW: A laboratory for the numerical exploration of spectra of linear operators
    • Carter J., Deconinck B., Kiyak F., and Kutz J.N. SpectrUW: A laboratory for the numerical exploration of spectra of linear operators. Math. Comput. Simulation 74 (2007) 370-379
    • (2007) Math. Comput. Simulation , vol.74 , pp. 370-379
    • Carter, J.1    Deconinck, B.2    Kiyak, F.3    Kutz, J.N.4
  • 6
    • 10244243814 scopus 로고    scopus 로고
    • Spectra of positive and negative energies in the linearized NLS problem
    • Cuccagna S., Pelinovsky D., and Vougalter V. Spectra of positive and negative energies in the linearized NLS problem. Commun. Pure Appl. Math. 58 (2005) 1-29
    • (2005) Commun. Pure Appl. Math. , vol.58 , pp. 1-29
    • Cuccagna, S.1    Pelinovsky, D.2    Vougalter, V.3
  • 7
    • 33750370251 scopus 로고    scopus 로고
    • Computing spectra of linear operators using Hill's method
    • Deconinck B., and Kutz J.N. Computing spectra of linear operators using Hill's method. J. Comput. Phys. 219 (2006) 296-321
    • (2006) J. Comput. Phys. , vol.219 , pp. 296-321
    • Deconinck, B.1    Kutz, J.N.2
  • 8
    • 84972270667 scopus 로고
    • Instability of quasiperiodic solutions of the Ginzburg-Landau equation
    • Doelman A., Gardner R., and Jones C.K.R.T. Instability of quasiperiodic solutions of the Ginzburg-Landau equation. Proc. Edinb. Math. Soc. 125 3 (1995) 501-517
    • (1995) Proc. Edinb. Math. Soc. , vol.125 , Issue.3 , pp. 501-517
    • Doelman, A.1    Gardner, R.2    Jones, C.K.R.T.3
  • 10
    • 36549088650 scopus 로고    scopus 로고
    • Orbital stability of periodic waves for the nonlinear Schrödinger equation
    • Gallay T., and Ha ̌ra ̌guş M. Orbital stability of periodic waves for the nonlinear Schrödinger equation. J. Dynam. Differential Equations 19 (2007) 825-865
    • (2007) J. Dynam. Differential Equations , vol.19 , pp. 825-865
    • Gallay, T.1    Ha ̌ra ̌guş, M.2
  • 11
    • 33846331701 scopus 로고    scopus 로고
    • Stability of small periodic waves for the nonlinear Schrödinger equation
    • Gallay T., and Ha ̌ra ̌guş M. Stability of small periodic waves for the nonlinear Schrödinger equation. J. Differential Equations 234 (2007) 544-581
    • (2007) J. Differential Equations , vol.234 , pp. 544-581
    • Gallay, T.1    Ha ̌ra ̌guş, M.2
  • 12
    • 0031285528 scopus 로고    scopus 로고
    • Spectral analysis of long wavelength periodic waves and applications
    • Gardner R. Spectral analysis of long wavelength periodic waves and applications. J. Reine Angew. Math. 491 (1997) 149-181
    • (1997) J. Reine Angew. Math. , vol.491 , pp. 149-181
    • Gardner, R.1
  • 14
    • 84990563336 scopus 로고
    • Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system
    • Grillakis M. Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system. Commun. Pure Appl. Math. 43 (1990) 299-333
    • (1990) Commun. Pure Appl. Math. , vol.43 , pp. 299-333
    • Grillakis, M.1
  • 15
    • 84990623184 scopus 로고
    • Linearized instability for nonlinear Schrödinger and Klein-Gordon equations
    • Grillakis M. Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Commun. Pure Appl. Math. 46 (1988) 747-774
    • (1988) Commun. Pure Appl. Math. , vol.46 , pp. 747-774
    • Grillakis, M.1
  • 16
    • 0000468151 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry, I
    • Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in the presence of symmetry, I. J. Funct. Anal. 74 (1987) 160-197
    • (1987) J. Funct. Anal. , vol.74 , pp. 160-197
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 17
    • 29444432472 scopus 로고
    • Stability theory of solitary waves in the presence of symmetry, II
    • Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in the presence of symmetry, II. J. Funct. Anal. 94 (1990) 308-348
    • (1990) J. Funct. Anal. , vol.94 , pp. 308-348
    • Grillakis, M.1    Shatah, J.2    Strauss, W.3
  • 18
    • 1642485104 scopus 로고    scopus 로고
    • Slow damping of internal waves in a stably stratified fluid
    • Gurski K., Kollár R., and Pego R. Slow damping of internal waves in a stably stratified fluid. Proc. R. Soc. Lond. A 460 (2004) 977-994
    • (2004) Proc. R. Soc. Lond. A , vol.460 , pp. 977-994
    • Gurski, K.1    Kollár, R.2    Pego, R.3
  • 19
    • 0000670781 scopus 로고
    • Instability of standing waves for non-linear Schrödinger-type equations
    • Jones C.K.R.T. Instability of standing waves for non-linear Schrödinger-type equations. Ergodic Theory Dynam. Systems 8 (1988) 119-138
    • (1988) Ergodic Theory Dynam. Systems , vol.8 , pp. 119-138
    • Jones, C.K.R.T.1
  • 20
    • 3342994344 scopus 로고    scopus 로고
    • Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
    • Kapitula T., Kevrekidis P., and Sandstede B. Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Physica D 195 3-4 (2004) 263-282
    • (2004) Physica D , vol.195 , Issue.3-4 , pp. 263-282
    • Kapitula, T.1    Kevrekidis, P.2    Sandstede, B.3
  • 21
    • 13244287967 scopus 로고    scopus 로고
    • Addendum: Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
    • Kapitula T., Kevrekidis P., and Sandstede B. Addendum: Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Physica D 201 1-2 (2005) 199-201
    • (2005) Physica D , vol.201 , Issue.1-2 , pp. 199-201
    • Kapitula, T.1    Kevrekidis, P.2    Sandstede, B.3
  • 22
    • 33846330123 scopus 로고
    • Instability of periodic waves described by the nonlinear Schrödinger equation
    • Kudashev V.P., and Mikhailovskii A.B. Instability of periodic waves described by the nonlinear Schrödinger equation. Zh. Eksp. Teor. Fiz. 90 (1986) 1656-1668
    • (1986) Zh. Eksp. Teor. Fiz. , vol.90 , pp. 1656-1668
    • Kudashev, V.P.1    Mikhailovskii, A.B.2
  • 23
    • 0141708278 scopus 로고
    • Stability of equilibria of Hamiltonian systems
    • MacKay R., and Meiss J. (Eds), Adam Hilger
    • MacKay R. Stability of equilibria of Hamiltonian systems. In: MacKay R., and Meiss J. (Eds). Hamiltonian Dynamical Systems (1987), Adam Hilger 137-153
    • (1987) Hamiltonian Dynamical Systems , pp. 137-153
    • MacKay, R.1
  • 25
    • 0003227202 scopus 로고
    • Introduction to the spectral theory of polynomial operator pencils
    • Amer. Math. Soc.
    • Markus A. Introduction to the spectral theory of polynomial operator pencils. Translation of Mathematical Monographs vol. 71 (1988), Amer. Math. Soc.
    • (1988) Translation of Mathematical Monographs , vol.71
    • Markus, A.1
  • 26
    • 51249112366 scopus 로고    scopus 로고
    • M. Oh, B. Sandstede, A. Yew, Stability of cnoidal waves for the focusing nonlinear Schrödinger equation with potential (in preparation)
    • M. Oh, B. Sandstede, A. Yew, Stability of cnoidal waves for the focusing nonlinear Schrödinger equation with potential (in preparation)
  • 27
    • 17144415970 scopus 로고    scopus 로고
    • Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations
    • Pelinovsky D. Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations. Proc. R. Soc. Lond. A 461 (2005) 783-812
    • (2005) Proc. R. Soc. Lond. A , vol.461 , pp. 783-812
    • Pelinovsky, D.1
  • 29
    • 33846303851 scopus 로고
    • On the stability of solutions of the non-linear Schrödinger equation
    • Rowlands G. On the stability of solutions of the non-linear Schrödinger equation. IMA J. Appl. Math. 13 (1974) 367-377
    • (1974) IMA J. Appl. Math. , vol.13 , pp. 367-377
    • Rowlands, G.1
  • 30
    • 33745697454 scopus 로고    scopus 로고
    • Eigenvalues of zero energy in the linearized NLS problem
    • Vougalter V., and Pelinovsky D. Eigenvalues of zero energy in the linearized NLS problem. J. Math. Phys. 47 (2006) 062701
    • (2006) J. Math. Phys. , vol.47 , pp. 062701
    • Vougalter, V.1    Pelinovsky, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.