24 citations · 57 across the 11 of their papers we have counts for
13 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-…
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…
Lie-Bäcklund symmetry and non-invariant solutions of nonlinear evolution equations
Ivan M. Tsyfra, Wojciech Rzeszut, Vsevolod A. Vladimirov
We study the symmetry reduction of nonlinear partial differential equations which are used for describing diffusion processes in nonhomogeneous medium. We find ansatzes reducing pa…
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…
Solitary waves in the model of active media, taking into account relaxing effects
Wojciech Likus, Vsevolod A. Vladimirov
We study a system of differential equation simulating transport phenomena in active structured media. The model is a generalization of the McKean s modification of the celebrated F…