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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 643–658 (Mi mz4062)  

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

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

DOI: https://doi.org/10.4213/mzm4062

Full text: PDF file (546 kB)
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English version:
Mathematical Notes, 2009, 86:5, 612–624

Bibliographic databases:

UDC: 517.98
Received: 29.05.2007
Revised: 01.06.2009

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 articles:
    1. Kapitula T., Hibma E., Kim H.-P., Timkovich J., “Instability Indices for Matrix Polynomials”, Linear Alg. Appl., 439:11 (2013), 3412–3434  crossref  mathscinet  zmath  isi  scopus
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