An Additional Gibbs' State for the Cubic Schrodinger Equation on the Circle

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dc.creatorVaninsky, K. L.
dc.date2000-09-07
dc.date.accessioned2026-07-07T05:33:01Z
dc.date.available2026-07-07T05:33:01Z
dc.descriptionAn invariant Gibbs' state for the nonlinear Schrodinger equation on the circle was constructed by Bourgain, and McKean, out of the basic Hamiltonian using a trigonometric cut-off. The cubic nonlinear Schrodinger equation is a completely integrable system having an infinite number of additional integrals of motion. In this paper we construct the second invariant Gibbs' state from one of these additional integrals for the cubic NLS on the circle. This additional Gibbs' state is singular with respect to the Gibbs' state previously constructed from the basic Hamiltonian. Our approach employs the Ablowitz-Ladik system, a completely integrable discretization of the cubic Schrodinger equation.
dc.description50 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/nlin/0009019
dc.identifierhttp://arxiv.org/abs/nlin/0009019
dc.identifierCPAM, vol LIV, 0537-0582 (2001)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79860
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.titleAn Additional Gibbs' State for the Cubic Schrodinger Equation on the Circle
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