22 citations · 38 across the 7 of their papers we have counts for
9 papers
Solitary wave dynamics governed by the modified FitzHugh-Nagumo equation
Aleksandra Gawlik, Sergii Skurativskyi, Vsevolod Vladimirov
The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work that the model, under c…
Existence of the solitary wave solutions supported by the hyperbolic modification of the FitzHugh-Nagumo system
Aleksandra Gawlik, Vsevolod Vladimirov, Sergii Skurativskyi
We study a system of nonlinear differential equations simulating transport phenomena in active media. The model we are interested in is a generalization of the celebrated FitzHugh-…
Properties of impact events in the model of forced impacting oscillator: experimental and numerical investigations
Sergii Skurativskyi, Grzegorz Kudra, Grzegorz Wasilewski +1
The paper deals with the studies of forced impacting oscillator when are taken into account the dry and viscous resistance, as well as the generalized Hertz contact law during an i…
Statistical properties of shear deformation of granular media and analogies with natural seismic processes
S. V. Mykulyak, V. V. Polyakovskyi, S. I Skurativskyi
In this paper, the process of shear deformation of the medium formed by the cubic grains is investigated experimentally. It is demonstrated that the deformation process is intermit…
On the spectral stability of soliton-like solutions to a non-local hydrodynamic-type model
Vsevolod A. Vladimirov, Sergii Skurativskyi
A model of nonlinear elastic medium with internal structure is considered. The medium is assumed to contain cavities, microcracks or blotches of substances that differ sharply in p…
The class of second order quasilinear equations: models, solutions and background of classification
O. Makarenko, A. Popov, S. Skurativskyi
The paper is concerned with the unsteady solutions to the model of mutually penetrating continua and quasilinear hyperbolic modification of the Burgers equation (QHMB). The studies…
Compacton solutions and (non)integrability for nonlinear evolutionary PDEs associated with a chain of prestressed granules
A. Sergyeyev, S. Skurativskyi, V. Vladimirov
We present the results of study of a nonlinear evolutionary PDE (more precisely, a one-parameter family of PDEs) associated with the chain of pre-stressed granules. The PDE in ques…
Solitary waves in one-dimensional pre-stressed lattice and its continual analog
Vsevolod Vladimirov, Sergii Skurativskyi
One of the most interesting phenomena occuring in nonlinear media models is the existence of wave patterns, such as kinks, solitons, compactons, peakons and many others. There are…
On the dynamics of solitary wave solutions supported by the model of mutually penetrating continua
Sergii Skurativskyi, Vjacheslav Danylenko
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscill…