Thet→∞ asymptotic regime of the Cauchy problem solution for the Toda chain with threshold-type Initial data

We obtain formulas allowing us to find solutions of the Toda chain using the inverse scattering transform method and investigate the t→∞ asymptotic behavior of the solutions. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 3, pp. 429–440, June, 1999     

Rapidly Decreasing Solution of the Initial Boundary-Value Problem for the Toda Lattice

Using the inverse scattering transform, we investigate an initial boundary-value problem with zero boundary condition for the Toda lattice. We prove the existence and uniqueness of a rapidly decreasing solution and determine a class of initial data that guarantees the existence of a rapidly decreasing solution. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1144 – 1152, August, 2005.     

On the Inverse Scattering Problem for the One-Dimensional Schrödinger Equation with Increasing Potential

Ukrainian Mathematical Journal - We consider a one-dimensional Schrödinger equation on the entire axis whose potential rapidly decreases on the left-hand side and infinitely increases on the...     

Transformation Operators for the Perturbed Hill Difference Equation and One of Their Applications

We construct transformation operators with conditions at infinity for the perturbed Hill equation. We give one application of transformation operators to studying solutions of some nonlinear difference equation.     

Global attractors for the plate equation with a localized damping and a critical exponent in an unbounded domain

In this paper, we study the asymptotic behavior of solutions for the plate equation with a localized damping and a critical exponent. We prove the existence, regularity and finite dimensionality of a global attractor in .     

A unique continuation result for the plate equation and an application

In this paper, we prove the unique continuation property for the weak solution of the plate equation with the low regular coefficient. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping. Copyright © 2015 John Wiley & Sons, Ltd.     

Transformation Operators for Perturbed Harmonic Oscillators

Mathematical Notes - The equation describing a perturbed harmonic oscillator is considered. Using transformation operators, we obtain representations of solutions of this equation with conditions...