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Azizov, T. Ya.; Chugunova, M. V.

Pontryagin’s theorem and spectral stability analysis of solitons. (English. Russian original) Zbl 1182.35192

Math. Notes 86, No. 5, 612-624 (2009); translation from Mat. Zametki 86, No. 5, 643-658 (2009).
Summary: 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).

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MSC:

35Q51 Soliton equations
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35B35 Stability in context of PDEs
35C08 Soliton solutions

Keywords:

Hamiltonian system; linearization; stability; unstable eigenvalue; existence criterion; Pontryagin space; soliton; block representation; Hilbert space
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References:

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