2019
Том 71
№ 1

# Samoilenko Yu. I.

Articles: 10
Article (Ukrainian)

### Asymptotic $Σ$-solutions to singularly perturbed Benjamin – Bona – Mahony equation with variable coefficients

Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 236-254

We study the problem of construction of asymptotic $\Sigma$ -solutions to the singularly perturbed Benjamin – Bona – Mahony equation with variable coefficients. An algorithm for the construction of solutions is described. We determine main and first terms of the asymptotic solution. The theorems on the accuracy with which the indicated asymptotic solution satisfies the considered equation are also proved.

Article (Ukrainian)

### Asymptotic Multiphase Solitonlike Solutions of the Cauchy Problem for a Singularly Perturbed Korteweg–de-Vries Equation with Variable Coefficients

Ukr. Mat. Zh. - 2014. - 66, № 12. - pp. 1640–1657

We describe the set of initial conditions under which the Cauchy problem for a singularly perturbed Korteweg–de-Vries equation with variable coefficients has an asymptotic multiphase solitonlike solution. The notion of manifold of initial values for which the above-mentioned solution exists is proposed for the analyzed Cauchy problem. The statements on the estimation of the difference between the exact and constructed asymptotic solutions are proved for the Cauchy problem.

Article (Ukrainian)

### Two-Phase Solitonlike Solutions of the Cauchy Problem for a Singularly Perturbed Korteweg-De-Vries Equation with Variable Coefficients

Ukr. Mat. Zh. - 2013. - 65, № 11. - pp. 1515–1530

We describe a set of initial conditions for which the Cauchy problem for a singularly perturbed Korteweg–de-Vries equation with variable coefficients has an asymptotic two-phase solitonlike solution. The notion of the manifold of initial data of the Cauchy problem for which this solution exists is proposed.

Article (Ukrainian)

### Asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg?de Vries equation with variable coefficients. II

Ukr. Mat. Zh. - 2012. - 64, № 8. - pp. 1089-1105

We consider the problem of the construction of higher terms of asymptotic many-phase soliton-type solutions of the singular perturbed Korteweg – de Vries equation with variable coefficients. The accuracy with which the obtained asymptotic solution satisfies the original equation is determined.

Article (Ukrainian)

### Asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg?de Vries equation with variable coefficients

Ukr. Mat. Zh. - 2012. - 64, № 7. - pp. 970-87

We propose an algorithm for the construction of asymptotic m-phase soliton-type solutions of a singularly perturbed Korteweg – de Vries equation with varying coefficients and establish the accuracy with which the main term asymptotically satisfies the considered equation.

Article (Ukrainian)

### Asymptotic two-phase solitonlike solutions of the singularly perturbed Korteweg-de Vries equation with variable coefficients

Ukr. Mat. Zh. - 2008. - 60, № 3. - pp. 388–397

We propose an algorithm of the construction of asymptotic two-phase soliton-type solutions of the Korteweg - de Vries equation with a small parameter at the higher derivative.

Article (Russian)

### Coherentization of the energy of heat fluctuations by a two-channel bilinear control system

Ukr. Mat. Zh. - 2007. - 59, № 11. - pp. 1557–1573

We propose and investigate a mathematical model of an open bilinear control system for the conversion of heat energy in a coherent form. We show that the use of a combinational parametric resonance formed by the control system in a one-temperature ensemble of weakly dissipative elastic-gyroscopic subsystems enables one to obtain a positive energy output without using any cooling device apart from the control system.

Anniversaries (Ukrainian)

### On the 90th birthday of Yurii Alekseevich Mitropol’skii

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 147–151

Article (Ukrainian)

### Asymptotic solutions of the Cauchy problem for the singularly perturbed Korteweg-de Vries equation with variable coefficients

Ukr. Mat. Zh. - 2007. - 59, № 1. - pp. 122–132

We propose an algorithm for the construction of an asymptotic solution of the Cauchy problem for the singularly perturbed Korteweg-de Vries equation with variable coefficients and prove a theorem on the estimation of its precision.

Article (Ukrainian)

### Asymptotic Expansions for One-Phase Soliton-Type Solutions of the Korteweg-De Vries Equation with Variable Coefficients

Ukr. Mat. Zh. - 2005. - 57, № 1. - pp. 111–124

We construct asymptotic expansions for a one-phase soliton-type solution of the Korteweg-de Vries equation with coefficients depending on a small parameter.