### Working paper

## Dual description of eta-deformed OSP sigma-models I

In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate large-amplitude, horizontally propagating internal solitary waves. Typically these waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of the Korteweg-de Vries type with

variable coecients. We shall review how these models are used to describe the propagation, deformation and disintegration of internal solitary waves as they propagate over the continental shelf and slope.

This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable deformations of meromorphic systems. Bibliography: 40 titles.

The paper discloses the method for estimating the deformation of fibroreticulate materials under the conditions of spatial multiaxial cyclic tension. The relevance of the method application for estimating the reliability performance of materials used for upholstering and finishing the interior of aircraft cabins has been justified. The equations of the elastic state of flexible fibroreticulate materials are obtained under the spatial tension in stresses and deformations. The geometric parameters of elastic deformations in the material during in the material in the design, processing treatment (molding process) and operation (shape stability) of the products. The advantage of the developed method of spatial cyclic tension of flexible fibroreticulate materials is the ability to model test conditions that simulate operating conditions. This capability of the test method allows to examine the dynamics of changes in the markers of the molding properties and shape stability of materials and to predict their behavior during operation.

We consider systems of linear differential equations discussing some classical and modern results in the Riemann problem, isomonodromic deformations, and other related topics. Against this background, we illustrate the relations between such phenomena as the integrability, the isomonodromy, and the Painlevé property. The recent advances in the theory of isomonodromic deformations presented show perfect agreement with that approach.

This aim of this paper is the interpretation of the results of mechanical testing of materials to determine their properties under hot deformation. As an example, a simulation of rod stretching in superplasticity mode was considered. Comparing obtained data with the analytical solution was conducted.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.