Irina Nizhnik
@imath.kiev.ua
Department of Differential Equations and Nonlinear Oscillations
Institute of Mathematics NAS of Ukraine
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics
11
Scopus Publications
97
Scholar Citations
5
Scholar h-index
4
Scholar i10-index
Scopus Publications
- Deterministic Diffusion
L. P. Nizhnik and I. L. Nizhnik
Springer Science and Business Media LLC - Differential Equations with Bistable Nonlinearity
A. M. Samoilenko and I. L. Nizhnik
Springer Science and Business Media LLC - Kinklike solutions of fourth-order differential equations with a cubic bistable nonlinearity
A. M. Samoilenko and I. L. Nizhnik
Pleiades Publishing Ltd - Periodic solutions of second-order differential equations with discontinuous nonlinearity
I. L. Nyzhnyk and A. O. Krasneeva
Springer Science and Business Media LLC - Stable stationary solutions for a reaction-diffusion equation with a multi-stable nonlinearity
Irene Nizhnik
Elsevier BV - Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries
S. Albeverio, G. Galperin, I.L. Nizhnik, and L.P. Nizhnik
Pleiades Publishing Ltd - Stable stationary solutions in reaction-diffusion systems consisting of a 1-D array of bistable cells
LEONID P. NIZHNIK, IRINA L. NIZHNIK, and MARTIN HASLER
World Scientific Pub Co Pte Lt
In this paper we present the construction of stable stationary solutions in reaction–diffusion systems consisting of a 1-D array of bistable cells with a cubic nonlinearity and with a cubic-like piecewise-linear nonlinearity. Some periodic solutions, kinks, solitons are considered. While it is known that spatial chaos arises in such systems with small coupling constants, we show the existence of spatial chaos for an arbitrary value of the cell coupling constant, in the case of the piecewise-linear nonlinearity. The value of the spatial entropy is found. We also show the existence of stable spatially periodic (pattern) solutions that persist for large coupling constants. - Spatial chaos in a fourth-order nonlinear parabolic equation
S. Albeverio and I.L. Nizhnik
Elsevier BV - A μ-oxo diiron(III) complex with a short Fe-Fe distance: Crystal structure of (μ-oxo)bis[N,N′-o-phenylenebis(salicylideneiminato)iron(III)]
Kenichi Oyaizu, Eniya Listiani Dewi, and Eishun Tsuchida
Elsevier BV - Stable solutions of a system of two connected Chua cells
I. L. Nizhnik
Springer Science and Business Media LLC - Soliton attraction law
I. L. Nizhnik
Springer Science and Business Media LLC
RECENT SCHOLAR PUBLICATIONS
- Deterministic diffusion in dynamical systems with a tiled phase space
I Nizhnik
arXiv preprint arXiv:2501.00182 2024 - Детермінована дифузія
IL Nizhnik, LP Nizhnik
Ukrains’ kyi Matematychnyi Zhurnal 71 (11), 1553-1569 2019 - Differential equations with bistable nonlinearity
AM Samoilenko, IL Nizhnik
Ukrainian Mathematical Journal 67, 584-624 2015 - Deterministic Diffusion
L Nizhnik, I Nizhnik
arXiv preprint arXiv:1501.00674 2015 - Kinklike solutions of fourth-order differential equations with a cubic bistable nonlinearity
AM Samoilenko, IL Nizhnik
Differential Equations 50, 203-212 2014 - Sergio Albeverio
S Albeverio, GA Galperin, IL Nizhnik, LP Nizhnik
2014 - Periodic solutions of second-order differential equations with discontinuous nonlinearity
I Nyzhnyk, Krasneeva
Journal of Mathematical Sciences 191 (3) 2013 - Stable stationary solutions for a reaction–diffusion equation with a multi-stable nonlinearity
I Nizhnik
Physics Letters A 357 (4-5), 319-322 2006 - Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries
SA Albeverio, GA Gal'perin, IL Nizhnik, LP Nizhnik
Regular and Chaotic Dynamics 10 (3), 285-306 2005 - Stable stationary solutions in reaction–diffusion systems consisting of a 1-d array of bistable cells
LP Nizhnik, IL Nizhnik, M Hasler
International Journal of Bifurcation and Chaos 12 (02), 261-279 2002 - Spatial chaos in a fourth-order nonlinear parabolic equation
S Albeverio, IL Nizhnik
Physics Letters A 288 (5-6), 299-304 2001 - Stable solutions of a system of two connected Chua cells
IL Nizhnik
Ukrainian Mathematical Journal 50 (11), 1789-1791 1998 - Stable difference scheme for a nonlinear Klein-Gordon equation
IL Nizhnik
Ukrainian Mathematical Journal 49 (6), 960-962 1997 - Soliton attraction law
IL Nizhnik
Ukrainian Mathematical Journal 47 (5), 789-792 1995 - Publication: Regular and Chaotic Dynamics Pub Date: 2005
S Albeverio, G Galperin, IL Nizhnik, LP Nizhnik
- Traveling avalanche waves in spatially discrete bistable reaction–diffusion systems
L Nizhnik, M Hasler, I Nizhnik
MOST CITED SCHOLAR PUBLICATIONS
- Stable stationary solutions in reaction–diffusion systems consisting of a 1-d array of bistable cells
LP Nizhnik, IL Nizhnik, M Hasler
International Journal of Bifurcation and Chaos 12 (02), 261-279 2002
Citations: 31 - Spatial chaos in a fourth-order nonlinear parabolic equation
S Albeverio, IL Nizhnik
Physics Letters A 288 (5-6), 299-304 2001
Citations: 27 - Periodic solutions of second-order differential equations with discontinuous nonlinearity
I Nyzhnyk, Krasneeva
Journal of Mathematical Sciences 191 (3) 2013
Citations: 14 - Differential equations with bistable nonlinearity
AM Samoilenko, IL Nizhnik
Ukrainian Mathematical Journal 67, 584-624 2015
Citations: 10 - Stable stationary solutions for a reaction–diffusion equation with a multi-stable nonlinearity
I Nizhnik
Physics Letters A 357 (4-5), 319-322 2006
Citations: 8 - Generalized billiards inside an infinite strip with periodic laws of reflection along the strip's boundaries
SA Albeverio, GA Gal'perin, IL Nizhnik, LP Nizhnik
Regular and Chaotic Dynamics 10 (3), 285-306 2005
Citations: 4 - Deterministic Diffusion
L Nizhnik, I Nizhnik
arXiv preprint arXiv:1501.00674 2015
Citations: 1 - Kinklike solutions of fourth-order differential equations with a cubic bistable nonlinearity
AM Samoilenko, IL Nizhnik
Differential Equations 50, 203-212 2014
Citations: 1 - Stable difference scheme for a nonlinear Klein-Gordon equation
IL Nizhnik
Ukrainian Mathematical Journal 49 (6), 960-962 1997
Citations: 1