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Matematicheskie Zametki, 2009, Volume 86, Issue 5, Pages 643–658
DOI: https://doi.org/10.4213/mzm4062 (Mi mzm4062) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Pontryagin's Theorem and Spectral Stability Analysis of Solitons

T. Ya. Azizova, M. V. Chugunovab

a Voronezh State University
b McMaster University
Full-text PDF (546 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm4062
Abstract: The main result of the present paper is the use of Pontryagin's theorem for proving a criterion, based on the difference in the number of negative eigenvalues between two self-adjoint operators $L_-$ and $L_+$, for the linear part of a Hamiltonian system to have eigenvalues with strictly positive real part (unstable eigenvalues).
Keywords: Hamiltonian system, linearization, stability, unstable eigenvalue, existence criterion, Pontryagin space, soliton, block representation, Hilbert space.
Received: 29.05.2007
Revised: 01.06.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 5, Pages 612–624
DOI: https://doi.org/10.1134/S0001434609110029
Bibliographic databases:
UDC: 517.98
Language: Russian
Citation: T. Ya. Azizov, M. V. Chugunova, “Pontryagin's Theorem and Spectral Stability Analysis of Solitons”, Mat. Zametki, 86:5 (2009), 643–658; Math. Notes, 86:5 (2009), 612–624
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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