24 citations · 57 across the 11 of their papers we have counts for
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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…
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…
Stability and dynamical features of solitary wave solutions for a hydrodynamic-type system taking into account non-local effects
Vsevolod Vladimirov, Czesław Maczka, Artur Sergyeyev +1
We consider a hydrodynamic-type system of balance equations which is closed by the dynamic equation of state taking into account the effects of spatial nonlocality. Symmetry and lo…
On the non-local hydrodynamic-type system and its soliton-like solution
V. A. Vladimirov, E. V. Kutafina, B. Zorychta
We analyze the conditions, which guarantee the existence of periodic and soliton-like traveling wave solutions in the non-local hydrodynamic model of structured media.