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Volumn 5, Issue 1, 2006, Pages 66-83

Block-diagonalization of the symmetric first-order coupled-mode system

Author keywords

Eigenvalues; Gap solitons; Hamiltonian first order coupled mode systems; Invariant subspaces; Spectral stability

Indexed keywords

ATOMIC PHYSICS; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; LINEAR EQUATIONS; OPTICS;

EID: 33644887197     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/050629781     Document Type: Article
Times cited : (37)

References (24)
  • 4
    • 0000764814 scopus 로고    scopus 로고
    • Coupled-mode theory for light propagation through deep nonlinear gratings
    • C. M. DE STERKE, D. G. SALINAS, AND J. E. SIPE, Coupled-mode theory for light propagation through deep nonlinear gratings, Phys. Rev. E, 54 (1996), pp. 1969-1989.
    • (1996) Phys. Rev. E , vol.54 , pp. 1969-1989
    • De Sterke, C.M.1    Salinas, D.G.2    Sipe, J.E.3
  • 5
    • 25144501646 scopus 로고    scopus 로고
    • Modeling of wave resonances in low-contrast photonic crystals
    • D. AGUEEV AND D. PELINOVSKY, Modeling of wave resonances in low-contrast photonic crystals, SIAM J. Appl. Math., 65 (2005), pp. 1101-1129.
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 1101-1129
    • Agueev, D.1    Pelinovsky, D.2
  • 6
    • 37649031143 scopus 로고    scopus 로고
    • Bifurcations and stability of gap solitons in periodic potentials
    • D. E. PELINOVSKY, A. A. SUKHORUKOV, AND YU. S. KIVSHAR, Bifurcations and stability of gap solitons in periodic potentials, Phys. Rev. E, 70 (2004), 036618.
    • (2004) Phys. Rev. E , vol.70 , pp. 036618
    • Pelinovsky, D.E.1    Sukhorukov, A.A.2    Kivshar, Yu.S.3
  • 7
    • 11744322885 scopus 로고    scopus 로고
    • Vibrations and oscillatory instabilities of gap solitons
    • I. V. BARASHENKOV, D. E. PELINOVSKY, AND E. V. ZEMLYANAYA, Vibrations and oscillatory instabilities of gap solitons, Phys. Rev. Lett., 80 (1998), pp. 5117-5120.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 5117-5120
    • Barashenkov, I.V.1    Pelinovsky, D.E.2    Zemlyanaya, E.V.3
  • 8
    • 0034174197 scopus 로고    scopus 로고
    • Oscillatory instabilities of gap solitons: A numerical study
    • I. V. BARASHENKOV AND E. V. ZEMLYANAYA, Oscillatory instabilities of gap solitons: A numerical study, Comput. Phys. Comm., 126 (2000), pp. 22-27.
    • (2000) Comput. Phys. Comm. , vol.126 , pp. 22-27
    • Barashenkov, I.V.1    Zemlyanaya, E.V.2
  • 9
    • 0030554227 scopus 로고    scopus 로고
    • The squared eigenfunctions of the massive Thirring model in laboratory coordinates
    • D. J. KAUF AND T. I. LAKOBA, The squared eigenfunctions of the massive Thirring model in laboratory coordinates, J. Math. Phys., 37 (1996), pp. 308-323.
    • (1996) J. Math. Phys. , vol.37 , pp. 308-323
    • Kauf, D.J.1    Lakoba, T.I.2
  • 10
    • 0030538778 scopus 로고    scopus 로고
    • Variational method: How it can generate false instabilities
    • D. J. KAUF AND T. I. LAKOBA, Variational method: How it can generate false instabilities, J. Math. Phys., 37 (1996), pp. 3442-3462.
    • (1996) J. Math. Phys. , vol.37 , pp. 3442-3462
    • Kauf, D.J.1    Lakoba, T.I.2
  • 11
    • 0343897880 scopus 로고    scopus 로고
    • On the stability of gap solitons
    • J. SCHOLLMANN, On the stability of gap solitons, Phys. A, 288 (2000), pp. 218-224.
    • (2000) Phys. A , vol.288 , pp. 218-224
    • Schollmann, J.1
  • 12
    • 0342364342 scopus 로고    scopus 로고
    • Stability analysis for extended models of gap solitary waves
    • J. SCHOLLMANN AND A. P. MAYER, Stability analysis for extended models of gap solitary waves, Phys. Rev. E, 61 (2000), pp. 5830-5838.
    • (2000) Phys. Rev. E , vol.61 , pp. 5830-5838
    • Schollmann, J.1    Mayer, A.P.2
  • 13
    • 0036373932 scopus 로고    scopus 로고
    • Edge bifurcations for near integrable systems via Evans function techniques
    • T. KAPITULA AND B. SANDSTEDE, Edge bifurcations for near integrable systems via Evans function techniques, SIAM J. Math. Anal., 33 (2002), pp. 1117-1143.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1117-1143
    • Kapitula, T.1    Sandstede, B.2
  • 14
    • 84867974985 scopus 로고    scopus 로고
    • Spectral analysis of stationary light transmission in nonlinear photonic structures
    • D. E. PELINOVSKY AND A. SCHEEL, Spectral analysis of stationary light transmission in nonlinear photonic structures, J. Nonlinear Sci., 13 (2003), pp. 347-396.
    • (2003) J. Nonlinear Sci. , vol.13 , pp. 347-396
    • Pelinovsky, D.E.1    Scheel, A.2
  • 15
    • 33644882810 scopus 로고    scopus 로고
    • A robust numerical method to study oscillatory instability of gap solitary waves
    • G. DERKS AND G. A. GOTTWALD, A robust numerical method to study oscillatory instability of gap solitary waves, SIAM J. Appl. Dyn. Syst., 4 (2005), pp. 140-158.
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , pp. 140-158
    • Derks, G.1    Gottwald, G.A.2
  • 16
    • 33644905988 scopus 로고    scopus 로고
    • Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons
    • D. J. B. LLOYD AND A. R. CHAMPNEYS, Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons, SIAM J. Sci. Comput., 27 (2005), pp. 759-773.
    • (2005) SIAM J. Sci. Comput. , vol.27 , pp. 759-773
    • Lloyd, D.J.B.1    Champneys, A.R.2
  • 17
    • 0003427216 scopus 로고    scopus 로고
    • Topics in bifurcation theory and applications, 2nd ed
    • World Scientific Publishing, River Edge, NJ
    • G. IOOSS AND M. ADELMEYER., Topics in Bifurcation Theory and Applications, 2nd ed., Advanced Ser. Nonlinear Dynam. 3, World Scientific Publishing, River Edge, NJ, 1998.
    • (1998) Advanced Ser. Nonlinear Dynam. , vol.3
    • Iooss, G.1    Adelmeyer, M.2
  • 18
    • 0013551127 scopus 로고
    • Singularities and groups in bifurcation theory, Vol. 2
    • Springer-Verlag, New York
    • M. GOLUBITSKY, I. STEWART, AND D. G. SCHAEFFER, Singularities and Groups in Bifurcation Theory, Vol. 2, Appl. Math. Sci. 69, Springer-Verlag, New York, 1988.
    • (1988) Appl. Math. Sci. , vol.69
    • Golubitsky, M.1    Stewart, I.2    Schaeffer, D.G.3
  • 19
    • 51249181717 scopus 로고
    • On the Coleman correspondence and the solution of the massive Thirring model
    • D. J. KAUF AND A. C. NEWELL, On the Coleman correspondence and the solution of the massive Thirring model, Lett. Nuovo Cimento, 20 (1977), pp. 325-331.
    • (1977) Lett. Nuovo Cimento , vol.20 , pp. 325-331
    • Kauf, D.J.1    Newell, A.C.2
  • 20
    • 17144415970 scopus 로고    scopus 로고
    • Inertia law for spectral stability of solitary waves in coupled nonlinear Schrodinger equations
    • D. E. PELINOVSKY, Inertia law for spectral stability of solitary waves in coupled nonlinear Schrodinger equations, Proc. Roy. Soc. London Ser. A, 461 (2005), pp. 783-812.
    • (2005) Proc. Roy. Soc. London Ser. A , vol.461 , pp. 783-812
    • Pelinovsky, D.E.1
  • 22
    • 0034321492 scopus 로고    scopus 로고
    • Eigenvalue computation in the 20th century
    • G. H. GOLUB AND H. A. VAN DER VORST, Eigenvalue computation in the 20th century, J. Comput. Appl. Math., 123 (2000), pp. 35-65.
    • (2000) J. Comput. Appl. Math. , vol.123 , pp. 35-65
    • Golub, G.H.1    Van Der Vorst, H.A.2
  • 23
    • 84936777186 scopus 로고
    • Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems
    • Y. SAAD, Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems, Math. Comp., 42 (1984), pp. 567-588.
    • (1984) Math. Comp. , vol.42 , pp. 567-588
    • Saad, Y.1
  • 24
    • 0344845500 scopus 로고    scopus 로고
    • Spectral methods in MATLAB
    • SIAM, Philadelphia
    • L. N. TREFETHEN, Spectral Methods in MATLAB, Software Environ. Tools 10, SIAM, Philadelphia, 2000.
    • (2000) Software Environ. Tools , vol.10
    • Trefethen, L.N.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.