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Dynamics of noncommutative solitons. I: Spectral theory and dispersive estimates. (English) Zbl 1345.81067

This work is the first part of an exhaustive series of papers devoted to the study of the dynamics of the discrete nonlinear Klein-Gordon equation and nonlinear Schrödinger equation with special Hamiltonians. More precisely, these Hamiltonians are second order difference operators with non-constant coefficients on \(\mathbb{Z}_+\). In this paper an estimate for the time decay of solutions of these operators to be \(t^{-1}\log^{-2} t\) is given.

MSC:

81R60 Noncommutative geometry in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
35C08 Soliton solutions

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References:

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