메뉴 건너뛰기




Volumn 4, Issue 1, 2005, Pages 140-158

A robust numerical method to study oscillatory instability of gap solitary waves

Author keywords

Edge bifurcation; Exterior algebra; Gap solitary wave; Massive Thirring model; Numerical Evans function; Oscillatory instability

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR ALGEBRA; PROBLEM SOLVING; SOLITONS;

EID: 33644882810     PISSN: 15360040     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/040605308     Document Type: Article
Times cited : (24)

References (24)
  • 1
    • 0002873156 scopus 로고
    • Self-induced transparency solitons in nonlinear refractive periodic media
    • A. B. ACEVES AND S. WABNITZ, Self-induced transparency solitons in nonlinear refractive periodic media, Phys. Lett., 141 (1989), pp. 37-42.
    • (1989) Phys. Lett. , vol.141 , pp. 37-42
    • Aceves, A.B.1    Wabnitz, S.2
  • 2
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of traveling waves
    • J. ALEXANDER, R. GARDNER, AND C. K. R. T. JONES, A topological invariant arising in the stability analysis of traveling waves, J. Reine Angew. Math., 410 (1990), pp. 167-212.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.K.R.T.3
  • 3
    • 0035982252 scopus 로고    scopus 로고
    • Numerical exterior algebra and the compound matrix method
    • L. ALLEN AND T. J. BRIDGES, Numerical exterior algebra and the compound matrix method, Numer. Math., 92 (2002), pp. 197-232.
    • (2002) Numer. Math. , vol.92 , pp. 197-232
    • Allen, L.1    Bridges, T.J.2
  • 4
    • 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
  • 5
    • 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
  • 6
    • 0035538197 scopus 로고    scopus 로고
    • Alternate Evans functions and viscous shock waves
    • S. BENZONI-GAVAGE, D. SERRE, AND K. ZUMBRUN, Alternate Evans functions and viscous shock waves, SIAM J. Math. Anal., 32 (2001), pp. 929-962.
    • (2001) SIAM J. Math. Anal. , vol.32 , pp. 929-962
    • Benzoni-Gavage, S.1    Serre, D.2    Zumbrun, K.3
  • 7
    • 0035646092 scopus 로고    scopus 로고
    • Numerical testing of the stability of viscous shock waves
    • L. Q. BRIN, Numerical testing of the stability of viscous shock waves, Math. Comp., 70 (2001), pp. 1071-1088.
    • (2001) Math. Comp. , vol.70 , pp. 1071-1088
    • Brin, L.Q.1
  • 8
    • 2142732118 scopus 로고    scopus 로고
    • Analytically varying eigenvectors and the stability of viscous shock waves
    • L. Q. BRIN AND K. ZUMBRUN, Analytically varying eigenvectors and the stability of viscous shock waves, Mat. Contemp., 22 (2002), pp. 19-32.
    • (2002) Mat. Contemp. , vol.22 , pp. 19-32
    • Brin, L.Q.1    Zumbrun, K.2
  • 9
    • 30244565104 scopus 로고
    • Soliton excitations in polyacetylene and relativistic field-theory models
    • D. K. CAMPBELL AND A. R. BISHOP, Soliton excitations in polyacetylene and relativistic field-theory models, Nuclear Phys. B, 200 (1982), pp. 297-328.
    • (1982) Nuclear Phys. B , vol.200 , pp. 297-328
    • Campbell, D.K.1    Bishop, A.R.2
  • 10
    • 0037112236 scopus 로고    scopus 로고
    • Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework
    • T. BRIDGES, G. DERKS, AND G. A. GOTTWALD, Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework, Phys. D, 172 (2003), pp. 190-216.
    • (2003) Phys. D , vol.172 , pp. 190-216
    • Bridges, T.1    Derks, G.2    Gottwald, G.A.3
  • 11
    • 0000224041 scopus 로고
    • Gap solitons
    • E. Wolf, ed., North-Holland, Amsterdam
    • C. M. DE STERKE AND J. E. SIPE, Gap solitons, in Progress in Optics, Vol. 33, E. Wolf, ed., North-Holland, Amsterdam, 1994, pp. 203-260.
    • (1994) Progress in Optics , vol.33 , pp. 203-260
    • De Sterke, C.M.1    Sipe, J.E.2
  • 12
    • 0016578299 scopus 로고
    • Nerve axon equations IV. the stable and unstable impulse
    • J. W. EVANS, Nerve axon equations IV. The stable and unstable impulse, Indiana, University Math. J., 24 (1975), pp. 1169-1190.
    • (1975) Indiana, University Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.W.1
  • 13
    • 0040942605 scopus 로고    scopus 로고
    • The gap lemma and geometric criteria for instability of viscous shock profiles
    • R. GARDNER AND K. ZUMBRUN, The gap lemma and geometric criteria for instability of viscous shock profiles, Comm. Pure Appl. Math., 51 (1998), pp. 797-855.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 797-855
    • Gardner, R.1    Zumbrun, K.2
  • 14
    • 0002348145 scopus 로고    scopus 로고
    • Stability of bright solitary wave solutions to perturbed nonlinear Schrödinger equations
    • T. KAPITULA AND B. SANDSTEDE, Stability of bright solitary wave solutions to perturbed nonlinear Schrödinger equations, Phys. D, 124 (1998), pp. 58-103.
    • (1998) Phys. D , vol.124 , pp. 58-103
    • Kapitula, T.1    Sandstede, B.2
  • 15
    • 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
  • 16
    • 0030554227 scopus 로고    scopus 로고
    • The squared eigenfunctions of the massive Thirring model in laboratory coordinates
    • D. J. KAUP 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
    • Kaup, D.J.1    Lakoba, T.I.2
  • 17
    • 0030538778 scopus 로고    scopus 로고
    • Variational method: How it can generate false instabilities
    • D. J. KAUP 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
    • Kaup, D.J.1    Lakoba, T.I.2
  • 19
    • 0008525467 scopus 로고
    • Exact localized solutions of two-dimensional field theories and massive fermions with Fermi interaction
    • S. Y. LEE, T. K. KUO, AND A. GAVRIELIDES, Exact localized solutions of two-dimensional field theories and massive fermions with Fermi interaction, Phys. Rev. D, 12 (1975), pp. 2249-2253.
    • (1975) Phys. Rev. D , vol.12 , pp. 2249-2253
    • Lee, S.Y.1    Kuo, T.K.2    Gavrielides, A.3
  • 20
    • 0001213434 scopus 로고
    • Fermion-field nontopological solitons
    • R. FRIEDBERG AND T. D. LEE, Fermion-field nontopological solitons, Phys. Rev. D, 15 (1977), pp. 1694-1711.
    • (1977) Phys. Rev. D , vol.15 , pp. 1694-1711
    • Friedberg, R.1    Lee, T.D.2
  • 23
    • 0346686985 scopus 로고    scopus 로고
    • Absolute and convective instabilities of waves on unbounded and large bounded domains
    • B. SANDSTEDE AND A. SCHEEL, Absolute and convective instabilities of waves on unbounded and large bounded domains, Phys. D, 145 (2000), pp. 233-277.
    • (2000) Phys. D , vol.145 , pp. 233-277
    • Sandstede, B.1    Scheel, A.2
  • 24
    • 0035343506 scopus 로고    scopus 로고
    • On the stability of travelling waves with large spatial period
    • B. SANDSTEDE AND A. SCHEEL, On the stability of travelling waves with large spatial period, J. Differential Equations, 172 (2001), pp. 134-188.
    • (2001) J. Differential Equations , vol.172 , pp. 134-188
    • Sandstede, B.1    Scheel, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.