Spectral asymptotics for the third order operator with periodic coefficients

2011/12/21 by Andrey Badanin, Badanin, Andrey, Evgeny Korotyaev +1 · 1 citation
Mathematics · Physics and Astronomy · #34L20 #34L40 #47E05 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:34L20 #msc:34L40 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1112.4973

30 pages, 3 figures

arxiv created 2011/12/21 · arxiv updated 2011/12/22

Abstract

We consider the self-adjoint third order operator with 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers the real line. We determine the high energy asymptotics of the periodic, anti-periodic eigenvalues and of the branch points of the Lyapunov function. Furthermore, in the case of small coefficients we show that either whole spectrum has multiplicity one or the spectrum has multiplicity one except for a small spectral nonempty interval with multiplicity three. In the last case the asymptotics of this small interval is determined.

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• Estimates, asymptotics and trace formulas for periodic vector NLS equations, II

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