# Third order operator with periodic coefficients on the real line

title={Third order operator with periodic coefficients on the real line},
author={Andrei Badanin and Evgeny L. Korotyaev},
journal={arXiv: Mathematical Physics},
year={2011}
}
• Published 20 December 2011
• Mathematics
• arXiv: Mathematical Physics
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…
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