메뉴 건너뛰기




Volumn 10, Issue 4, 2004, Pages 857-869

Eigenvalues and resonances using the Evans function

Author keywords

Evans function; Resonances

Indexed keywords


EID: 2942679820     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2004.10.857     Document Type: Article
Times cited : (33)

References (26)
  • 2
    • 0016369301 scopus 로고
    • The inverse scattering transform - Fourier analysis for nonlinear problems
    • M. Ablowitz, D. Kaup, A. Newell, and H. Segur. The inverse scattering transform - Fourier analysis for nonlinear problems. Stud. Appl. Math., 53(4):249-315, 1974.
    • (1974) Stud. Appl. Math. , vol.53 , Issue.4 , pp. 249-315
    • Ablowitz, M.1    Kaup, D.2    Newell, A.3    Segur, H.4
  • 3
    • 0021468830 scopus 로고
    • Perturbation of resonances in quantam mechanics
    • S. Albeverio and R. Høegh-Krohn. Perturbation of resonances in quantam mechanics. J. Math. Anal. Appl., 101:491-513, 1984.
    • (1984) J. Math. Anal. Appl. , vol.101 , pp. 491-513
    • Albeverio, S.1    Høegh-Krohn, R.2
  • 4
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability of travelling waves
    • J. Alexander, R. Gardner, and C.K.R.T. Jones. A topological invariant arising in the stability of travelling waves. J. Reine Angew. Math., 410:167-212, 1990.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.K.R.T.3
  • 5
    • 0000690474 scopus 로고    scopus 로고
    • Asymptotic distribution of resonances in one dimension
    • R. Froese. Asymptotic distribution of resonances in one dimension. J. Diff. Eqs., 137(2):251-272, 1997.
    • (1997) J. Diff. Eqs. , vol.137 , Issue.2 , pp. 251-272
    • Froese, R.1
  • 6
    • 0032363434 scopus 로고    scopus 로고
    • Upper bounds for the resonance counting function of schrödinger operators in odd dimensions
    • R. Froese. Upper bounds for the resonance counting function of Schrödinger operators in odd dimensions. Canad. J. Math., 50(3):538-546, 1998.
    • (1998) Canad. J. Math. , vol.50 , Issue.3 , pp. 538-546
    • Froese, R.1
  • 7
    • 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(7):797-855, 1998.
    • (1998) Comm. Pure Appl. Math. , vol.51 , Issue.7 , pp. 797-855
    • Gardner, R.1    Zumbrun, K.2
  • 8
    • 38249033043 scopus 로고
    • A unified approach to eigenvalues and resonances of schrödinger operators using fredholm determinants
    • F. Geztesy and H. Holden. A unified approach to eigenvalues and resonances of Schrödinger operators using Fredholm determinants. J. Math. Anal. Appl., 123:181-198, 1987.
    • (1987) J. Math. Anal. Appl. , vol.123 , pp. 181-198
    • Geztesy, F.1    Holden, H.2
  • 9
    • 0036994146 scopus 로고    scopus 로고
    • Perturbation of eigenvalues embedded at a threshold
    • A. Jensen and M. Melgaard. Perturbation of eigenvalues embedded at a threshold. Proc. Roy. Soc. Edinburgh, 132A:163-179, 2002.
    • (2002) Proc. Roy. Soc. Edinburgh , vol.132 A , pp. 163-179
    • Jensen, A.1    Melgaard, M.2
  • 10
    • 84967743294 scopus 로고
    • Stability of the travelling wave solutions of the Fitzhugh-Nagumo system
    • C.K.R.T. Jones. Stability of the travelling wave solutions of the Fitzhugh-Nagumo system. Trans. AMS, 286(2):431-469, 1984.
    • (1984) Trans. AMS , vol.286 , Issue.2 , pp. 431-469
    • Jones, C.K.R.T.1
  • 11
    • 0032622893 scopus 로고    scopus 로고
    • The Evans function and generalized Melnikov integrals
    • T. Kapitula. The Evans function and generalized Melnikov integrals. SIAM J. Math. Anal., 30(2):273-297, 1999.
    • (1999) SIAM J. Math. Anal. , vol.30 , Issue.2 , pp. 273-297
    • Kapitula, T.1
  • 12
    • 0033628312 scopus 로고    scopus 로고
    • Existence and stability of standing hole solutions to complex Ginzburg-Landau equations
    • T. Kapitula and J. Rubin. Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Nonlinearity, 13(1):77-112, 2000.
    • (2000) Nonlinearity , vol.13 , Issue.1 , pp. 77-112
    • Kapitula, T.1    Rubin, J.2
  • 13
    • 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. Physica D, 124(1-3):58-103, 1998.
    • (1998) Physica D , vol.124 , Issue.1-3 , pp. 58-103
    • Kapitula, T.1    Sandstede, B.2
  • 14
    • 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(5):1117-1143, 2002.
    • (2002) SIAM J. Math. Anal. , vol.33 , Issue.5 , pp. 1117-1143
    • Kapitula, T.1    Sandstede, B.2
  • 15
    • 0016962049 scopus 로고
    • Closure of the squared Zakharov-Shabat eigenstates
    • D. Kaup. Closure of the squared Zakharov-Shabat eigenstates. J. Math. Anal. Appl., 54:849-864, 1976.
    • (1976) J. Math. Anal. Appl. , vol.54 , pp. 849-864
    • Kaup, D.1
  • 16
    • 0016971835 scopus 로고
    • A perturbation expansion for the Zakharov-Shabat inverse scattering transform
    • D. Kaup. A perturbation expansion for the Zakharov-Shabat inverse scattering transform. SIAM J. Appl. Math., 31(1):121-133, 1976.
    • (1976) SIAM J. Appl. Math. , vol.31 , Issue.1 , pp. 121-133
    • Kaup, D.1
  • 17
    • 0001290416 scopus 로고
    • Perturbation theory for solitons in optical fibers
    • D. Kaup. Perturbation theory for solitons in optical fibers. Phys. Rev. A, 42(9):5689-5694, 1990.
    • (1990) Phys. Rev. A , vol.42 , Issue.9 , pp. 5689-5694
    • Kaup, D.1
  • 18
    • 2942682569 scopus 로고
    • Perturbation of resonances
    • A. Ramm. Perturbation of resonances. J. Math. Anal. Appl., 88:1-7, 1982.
    • (1982) J. Math. Anal. Appl. , vol.88 , pp. 1-7
    • Ramm, A.1
  • 19
    • 0001022241 scopus 로고
    • Perturbation theory for eigenvalues and resonances of schrödinger Hamiltonians
    • J. Rauch. Perturbation theory for eigenvalues and resonances of Schrödinger Hamiltonians. J. Func. Anal., 35:304-315, 1980.
    • (1980) J. Func. Anal. , vol.35 , pp. 304-315
    • Rauch, J.1
  • 22
    • 67649363651 scopus 로고    scopus 로고
    • chapter 18. Elsevier Science
    • B. Sandstede. Handbook of Dynamical Systems, volume 2, chapter 18, pages 983-1055. Elsevier Science, 2002.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 983-1055
    • Sandstede, B.1
  • 23
    • 0000931552 scopus 로고
    • Notes on infinite determinants of hilbert space operators
    • B. Simon. Notes on infinite determinants of Hilbert space operators. Adv. Math., 24:244-273, 1977.
    • (1977) Adv. Math. , vol.24 , pp. 244-273
    • Simon, B.1
  • 24
    • 37649004840 scopus 로고
    • On the absorption of eigenvalues by continuous spectrum in regular perturbation problems
    • B. Simon. On the absorption of eigenvalues by continuous spectrum in regular perturbation problems. J. Func. Anal., 25:338-344, 1977.
    • (1977) J. Func. Anal. , vol.25 , pp. 338-344
    • Simon, B.1
  • 25
    • 0011058107 scopus 로고    scopus 로고
    • Resonances in one dimension and Fredholm determinants
    • B. Simon. Resonances in one dimension and Fredholm determinants. J. Func. Anal., 178:396-420, 2000.
    • (2000) J. Func. Anal. , vol.178 , pp. 396-420
    • Simon, B.1
  • 26
    • 0001518892 scopus 로고    scopus 로고
    • Resonances in physics and geometry
    • M. Zworski. Resonances in physics and geometry. Notices Amer. Math. Soc., 46(3):319-328, 1999.
    • (1999) Notices Amer. Math. Soc. , vol.46 , Issue.3 , pp. 319-328
    • Zworski, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.