Geodesic
Pontryagin's Theorem and Spectral Stability Analysis of Solitons
Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 643-658

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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, Pontryagin space, block representation, Hilbert space.
Mots-clés : existence criterion, soliton 
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     author = {T. Ya. Azizov and M. V. Chugunova},
     title = {Pontryagin's {Theorem} and {Spectral} {Stability} {Analysis} of {Solitons}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--658},
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     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a0/}
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T. Ya. Azizov; M. V. Chugunova. Pontryagin's Theorem and Spectral Stability Analysis of Solitons. Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 643-658. http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a0/