Count of eigenvalues in the generalized eigenvalue problem

Journal of Mathematical Physics

Volumn 51, Issue 5, 2010, Pages

  Chugunova, Marina ^a   Pelinovsky, Dmitry ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77955266148     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3406252     Document Type: Article

References (32)

1. Azizov T. Iohvidov I.S. Elements of the Theory of Linear Operators in Spaces with Indefinite Metric 1986, and, (Nauka, Moscow).
2. Buslaev V.S. Perelman G.S. Scattering for the nonlinear Schrödinger equation: States close to a soliton. St. Petersbg. Math. J. 19934:1111. 1061-0022and
3. Cuccagna S. On asymptotic stability of ground states of nonlinear Schrödinger equations. Rev. Math. Phys. 200315:877. RMPHEX0129-055X10.1142/S0129055X03001849
4. Cuccagna S. Pelinovsky D. Vougalter V. Spectra of positive and negative energies in the linearized NLS problem. Commun. Pure Appl. Math. 200558:1. CPMAMV0010-364010.1002/cpa.20050and
5. Gantmacher F.P. Krein M.G. Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems 2002and(AMS ChelseaAMSProvidence).
6. Gelfand I.M. Lectures on Linear Algebra 1961(DoverNew York).
7. Glazman I.M. Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators 1965(Israel Program for Scientific TranslationJerusalem).
8. Gohberg I.G. Krein M.G. Introduction to the Theory of Linear Non-Self-Adjoint Operators 1969andTransactions Mathematical Monographs (AMSProvidence).
9. Grillakis M. Shatah J. Strauss W. Stability theory of solitary waves in the presence of symmetry. I. J. Funct. Anal. 198774:160. JFUAAW0022-123610.1016/0022-1236(87)90044-9and
10. Grillakis M. Shatah J. Strauss W. Stability theory of solitary waves in the presence of symmetry. II. J. Funct. Anal. 199094:308. JFUAAW0022-123610.1016/0022-1236(90)90016-Eand
11. Grillakis M. Linearized instability for nonlinear Schrödinger and Klein-Gordon equations. Commun. Pure Appl. Math. 198841:747. CPMAMV0010-364010.1002/cpa.3160410602
12. Grillakis M. Analysis of the linearization around a critical point of an infinite dimensional Hamiltonian system. Commun. Pure Appl. Math. 199043:299. CPMAMV0010-364010.1002/cpa.3160430302
13. Gurski K.F. Kollar R. Pego R.L. Slow damping of internal waves in a stably stratified fluid. Proc. R. Soc. London 2004460:977. PRLAAZ0962-844410.1098/rspa.2003.1226
14. Iohvidov I.S. Krein M.G. Langer H. Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric 1982and(Mathematische ForschungBerlin).
15. Kapitula T. Kevrekidis P. Sandstede B. Kapitula T. Kevrekidis P. Sandstede B. Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems. Physica D 2005201:199. PDNPDT0167-278910.1016/j.physd.2004.03.018PDNPDT0167-278910.1016/j.physd.2004.11.015and;
16. Kapitula T. Kevrekidis P.G. Linear stability of perturbed Hamiltonian systems: Theory and a case example. J. Phys. A 200437:7509. JPHAC50305-447010.1088/0305-4470/37/30/009and
17. Kato T. Perturbation Theory for Linear Operators 1976(Springer-VerlagBerlin).
18. Kodama Y. Pelinovsky D. Spectral stability and time evolution of N solitons in KdV hierarchy. J. Phys. A 200538:6129. JPHAC50305-447010.1088/0305-4470/38/27/003and
19. Krieger J. Schlag W. Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension. J. Am. Math. Soc. 200619:815. 0894-034710.1090/S0894-0347-06-00524-8
20. MacKay R.S. Stability of equilibria of Hamiltonian systems. Hamiltonian Dynamical Systems 1987137-153. R. S. MacKayJ. Meiss inedited by and (Adam HilgerBristol)
21. McLeod K. Uniqueness of positive radial solutions of Δu+f(u)=0 in Rn. Trans. Am. Math. Soc. 1993339:495. TAMTAM0002-994710.2307/2154282
22. Pego R.L. Warchall H.A. Spectrally stable encapsulated vortices for nonlinear Schrödinger equations. J. Nonlinear Sci. 200212:347. JNSCEK0938-879410.1007/s00332-002-0475-3and
23. Pelinovsky D.E. Inertia law for spectral stability of solitary waves in coupled nonlinear Schrödinger equations. Proc. R. Soc. LondonSer. A 2005461:783. PRLAAZ1364-502110.1098/rspa.2004.1345
24. Pelinovsky D.E. Kevrekidis P.G. Frantzeskakis D.J. Stability of discrete solitons in nonlinear Schrödinger lattices. Physica D 2005212:1. PDNPDT0167-278910.1016/j.physd.2005.07.021
25. Pelinovsky D.E. Kevrekidis P.G. Frantzeskakis D.J. Persistence and stability of discrete vortices in nonlinear Schrödinger lattices. Physica D 2005212:20. PDNPDT0167-278910.1016/j.physd.2005.09.015and
26. Pelinovsky D.E. Yang J. Instabilities of multihump vector solitons in coupled nonlinear Schrodinger equations. Stud. Appl. Math. 2005115:109. SAPMB60022-252610.1111/j.1467-9590.2005.01565and
27. Perelman G. Asymptotic stability of multi-soliton solutions for nonlinear Schrödinger equations. Commun. Partial Differ. Equ. 200429:1051. CPDIDZ0360-530210.1081/PDE-200033754
28. Perelman G. On the formation of singularities in solutions of the critical nonlinear Schrödinger equation. Ann. Henri Poincare 20012:605. AHPJFM1424-063710.1007/PL00001048
29. Pontryagin L.S. Hermitian operators in spaces with indefinite metric. Izv. Akad. Nauk SSSRSer. Mat. 19448:243. 0373-2436
30. Rodnianski I. Schlag W. Soffer A. Dispersive analysis of charge transfer models. Commun. Pure Appl. Math. 200558:149. CPMAMV0010-364010.1002/cpa.20066
31. Schlag W. Spectral theory and nonlinear partial differential equations: A survey. Discrete Contin. Dyn. Syst. 200615:703. 1078-094710.3934/dcds.2006.15.703
32. Schlag W. Stable manifolds for an orbitally unstable nonlinear Schrödinger equation. Ann. Math. 2009169:139. ANMAAH0003-486X10.4007/annals.2009.169.139