Galilean transformations and evolution of autowave fronts in external fields

V.A. Davydov^a, b, V.G. Morozov^a
^aMIREA - Russian Technological University, prosp. Vernadskogo 78, Moscow, 119454, Russian Federation
^bInstitute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation

We consider autowave regimes in two-dimensional excitable media in the presence of an external electric field, using Galilean transformations in the reaction-diffusion equations. It is shown that the transformation properties of these equations lead to some general relations for the autowave front and vortex drift velocities, independently of the concrete form of nonlinear terms in the equations. The general field dependence of the critical autowave characteristics is determined. Simple kinematic method discussed in this work is applicable for studying autowave evolution in three-dimensional and multicomponent excitable media.

PACS: 05.50.+q, 05.70.Ln, 82.40.−g, 87.10.+e (all)
DOI: 10.1070/PU1996v039n03ABEH000139
URL: https://ufn.ru/en/articles/1996/3/e/
Web of Science

A1996UL16500005
Citation: Davydov V A, Morozov V G "Galilean transformations and evolution of autowave fronts in external fields" Phys. Usp. 39 305–311 (1996)

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Оригинал: Давыдов В А, Морозов В Г «Галилеевы пpеобpазования и pаспpостpанение автоволновых фpонтов во внешних полях» УФН 166 327–334 (1996); DOI: 10.3367/UFNr.0166.199603e.0327

References (26) Cited by (6) Similar articles (20) ↓

G. Oppen “Objects and environment” Phys. Usp. 39 617–622 (1996)
A.B. Brailovskii, V.L. Vaks, V.V. Mityugov “Quantum models of relaxation” Phys. Usp. 39 745–750 (1996)
G.A. Martynov “Nonequilibrium statistical mechanics, transport equations, and the second law of thermodynamics” Phys. Usp. 39 1045–1070 (1996)
S.L. Sobolev “Local non-equilibrium transport models” Phys. Usp. 40 1043–1053 (1997)
V.B. Priezzhev “The dimer problem and the Kirchhoff theorem” Sov. Phys. Usp. 28 1125–1135 (1985)
Yu.L. Klimontovich “Relative ordering criteria in open systems” Phys. Usp. 39 1169–1179 (1996)
Ya.M. Blanter, M.I. Kaganov, D.V. Posvyanskii “De Haas-van Alphen effect as a first-order electronic topological transition” Phys. Usp. 38 203–209 (1995)
B.B. Kadomtsev “Classical and quantum irreversibility” Phys. Usp. 38 923–929 (1995)
I.E. Mazets “Kinetic equation including wave function collapses” Phys. Usp. 41 505–507 (1998)
V.V. Brazhkin, R.N. Voloshin et al “Phase equilibria in partially open systems under pressure: the decomposition of stoichiometric GeO₂ oxide” Phys. Usp. 46 1283–1289 (2003)
S.N. Semenov, M.E. Schimpf “Mass transport thermodynamics in nonisothermal molecular liquid mixtures” Phys. Usp. 52 1045–1054 (2009)
R.P. Poplavskii “Maxwell demon and the correspondence between information and entropy” Sov. Phys. Usp. 22 371–380 (1979)
S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles” Phys. Usp. 42 573–590 (1999)
I.I. Abbasov, B.M. Bolotovskii, V.A. Davydov “High-frequency asymptotic behavior of radiation spectra of moving charges in classical electrodynamics” Sov. Phys. Usp. 29 788–796 (1986)
B.M. Bolotovskii, V.A. Davydov, V.E. Rok “The emission of electromagnetic waves in the case of a smooth variation of parameters of a radiating system” Sov. Phys. Usp. 25 167–175 (1982)
B.M. Bolotovskii, V.A. Davydov, V.E. Rok “Radiation of electromagnetic waves on instantaneous change of the state of the radiating system” Sov. Phys. Usp. 21 865–872 (1978)
V.P. Bykov, A.V. Gerasimov, V.O. Turin “Coulomb disintegration of weak electron fluxes and the photocounts” Phys. Usp. 38 911–921 (1995)
Yu.M. Kopnin, M.Yu. Kopnin “Orbits of the hydrogen electron in a uniform electric field” Phys. Usp. 36 (11) 1075–1078 (1993)
G.N. Gaidukov, A.A. Abramov “An interpretation of the energy conservation law for a point charge moving in a uniform electric field” Phys. Usp. 51 163–166 (2008)
M.Ya. Agre “Multipole expansions in magnetostatics” Phys. Usp. 54 167–180 (2011)

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