A. I. Komech

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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)
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)
We consider the dynamics of a harmonic crystal in d dimensions with n components , d, n arbitrary, d, n ≥ 1 , and study the distribution µ t of the solution at time t ∈ R. The initial measure µ 0 has a translation-invariant correlation matrix, zero mean, and finite mean energy density. It also satisfies a Rosenblatt-resp. Ibragimov-Linnik type mixing(More)
Consider the wave equation with constant or variable coefficients in IR 3. The initial datum is a random function with a finite mean density of energy that also satisfies a Rosenblatt-or Ibragimov-Linnik-type mixing condition. The random function converges to different space-homogeneous processes as x 3 → ±∞ , with the distributions µ ±. We study the(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)
the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the(More)