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The paper considers the wave equation, with constant or variable coefficients in R n , with odd n \ 3. We study the asymptotics of the distribution m t of the random solution at time t ¥ R as t Q .. It is assumed that the initial measure m 0 has zero mean, translation-invariant covariance matrices, and finite expected energy density. We also assume that m 0(More)
Consider the Klein-Gordon equation (KGE) in IR n , n ≥ 2, with constant or variable coefficients. We study the distribution µ t of the random solution at time t ∈ IR. We assume that the initial probability measure µ 0 has zero mean, a translation-invariant covariance, and a finite mean energy density. We also asume that µ 0 satisfies a Rosenblatt-or(More)
We consider the dynamics of a harmonic crystal in d dimensions with n components , d, n ≥ 1. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt-or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as x d → ±∞ , with the distributions µ ±.(More)
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schrödinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U (1). For initial states close to a solitary wave, the solution converges to a sum of another solitary wave and dispersive wave which is a solution to(More)
We consider the dynamics of a field coupled to a harmonic crystal with n components in dimension d , d, n ≥ 1. The crystal and the dynamics are translation-invariant with respect to the subgroup Z Z d of IR d. The initial data is a random function with a finite mean density of energy which also satisfies a Rosenblatt-or Ibragimov-Linnik-type mixing(More)
We consider the Dirac equation in IR 3 with constant coefficients and study the distribution µ t of the random solution at time t ∈ IR. It is assumed that the initial measure µ 0 has zero mean, a translation-invariant covariance, and finite mean charge density. We also assume that µ 0 satisfies a mixing condition of Rosenblatt-or Ibragimov-Linnik-type. The(More)
We consider the Schrödinger-Poisson-Newton equations for crystals with one ion per cell. We linearize this dynamics at the periodic minimizers of energy per cell and introduce a novel class of the ion charge densities that ensures the stability of the linearized dynamics. Our main result is the energy positivity for the Bloch generators of the linearized(More)
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