Third order operator with periodic coefficients on the real line

2011/12/20 by Andrey Badanin, A. Badanin, Badanin, A. +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #34L10 #34L20 #47E05 #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories #math-ph #math.MP #msc:34L10 #msc:34L20 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1112.4587

24 pages, in Russian

arxiv created 2011/12/20 · openalex publication_date 2011/12/20 · arxiv updated 2011/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the third order operator with periodic coefficients on the real line. This operator is used in the integration of the non-linear evolution Boussinesq equation. For the minimal smoothness of the coefficients we prove that: 1) the operator is self-adjoint and it is decomposable into the direct integral, 2) the spectrum is absolutely continuous, fills the whole real axis, and has multiplicity one or three, 3) the Lyapunov function, analytic on a three-sheeted Riemann surface, is constructed and researched, 4) the spectrum of multiplicity three is bounded and it is described in terms of some entire function (the discriminant).

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

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