Probabilistic methods for discrete nonlinear Schrödinger equations

Abstract

We show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation are exactly solvable in dimensions three and higher. A number of explicit formulas are derived.

30 pages, 2 figures. To appear in Comm. Pure Appl. Math

References in corpus (5)

• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
• Ill-posedness for nonlinear Schrodinger and wave equations
• Invariant measures for the defocusing NLS
• Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate
• Interpolation of Gibbs measures with White Noise for Hamiltonian PDE