In the paper, we study entire solutions of the difference equation Ïˆ (z + h) = M (z) Ïˆ (z), z âˆˆ C, Ïˆ (z) âˆˆ C 2. In this equation, h is a fixed positive parameter, and M : C â†’ SL (2, C) is a givenâ€¦ (More)

The long-time asymptotics is analyzed for finite energy solutions of the 1D SchrÃ¶dinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotationâ€¦ (More)

We prove two new identities in scattering theory in Hamiltonian mechanics and discuss the analogy between these identities and their counterparts in quantum scattering theory. These identitiesâ€¦ (More)

The long-time asymptotics is analyzed for finite energy solutions of the 1D SchrÃ¶dinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotationâ€¦ (More)

We are interested in the asymptotic behavior of the solution to the Cauchy problem for the linear evolution equation iÎµâˆ‚tÏˆ = A(t)Ïˆ, A(t) = A0 + V (t), Ïˆ(0) = Ïˆ0, in the limit Îµ â†’ 0. A case of specialâ€¦ (More)

A system of three one-dimensional quantum particles with Coulomb pairwise interaction is treated. A scattered plane wave type asymptotic description at infinity in the configuration space ofâ€¦ (More)

Basing on analogy between the three-body scattering problem and the diffraction problem of the plane wave (for the case of the short range pair potentials) by the system of six half transparentâ€¦ (More)