Third order operator with periodic coefficients on the real line

Details Third order operator with periodic coefficients on the real line Third order operator with periodic coefficients on the real line

2011-12-20

arxiv.org/abs/1112.4587v1

Physics

Mathematical Physics

24 pages, in Russian

Scientific paper

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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