Exact solutions for the kinematic model of autowaves in two-dimensional excitable media

Physica D: Nonlinear Phenomena

Volumn 94, Issue 4, 1996, Pages 205-220

  Brazhnik, Pavel K ^a,b  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Dynamics of interfaces; Inhomogeneous media; Motion forced by curvature; Traveling waves

Indexed keywords

EID: 22244443853     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(96)00042-5     Document Type: Article

References (26)

1. A.S Mikhailov, Foundations of Synergetics. I. Distributed Active Systems (Springer, Berlin, 1990).
2. A. Holden, M. Markus and H. Othmer, eds., Nonlinear Wave Processes in Excitable media (Plenum, New York, 1990).
3. H.L. Swinney and V.I. Krinsky, eds., Wave and patterns in chemical and biological media, Physica D 49 (1,2) (1991).
4. A.M. Zhabotinsky, M.D. Eager and I.R. Epstein, Phys. Rev. Letts. 71 (1993) 1526.
5. O. Steinbock, V.S. Zykov and S.C. Muller, Phys. Rev. E 48 (1993) 3295.
6. A.S. Mikhailov and V.S. Zykov, Physica D 52 (1992) 379.
7. E. Meron and P. Pelce, Phys. Rev. Lett. 60 (1988) 1880.
8. P.K. Brazhnik, V.A. Davydov and A.S. Mikhailov, Theor. Math. Phys. 74 (1988) 300.
9. V.A. Davydov, V.S. Zykov and A.S. Mikhailov, Sov. Phys. Usp. 34 (1991) 665;
10. Physica D 70 (1994) 1.
11. E. Meron, Phys. Rep. 218 (1992) 1.
12. V.S. Zykov, Biophysics 25 (1980) 906.
13. P. Foerster, S. Muller and B. Hess, Science 241 (1988) 685;
14. Proc. Natl. Acad. Sci. USA 86 (1989) 6831.
15. P.K. Rashevsky, Course of Differential Geometry (Fizmatgiz, Moscow, 1956).
16. Ya.B. Zeldovich and B. Malomed, Sov. Phys. Dokl. 29 (1980) 721.
17. G. Sansone and R. Conti, Non-linear Differential Equations (Pergamon Press, New York, 1964).
18. E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen (Chelsea, New York, 1948).
19. P.K. Brazhnik and V.A. Davydov, Physics Lett. A 199 (1995) 40.
20. E. Whitham, Linear and nonlinear waves (J Wiley, New York, 1974).
21. R.E. Goldstein and D.M. Petrich, Phys. Rev. Lett. 67 (1991) 3202.
22. J.D. Logan, An Introduction to Nonlinear Differential Equations (J Wiley, New York, 1994).
23. P.C. Fife, Dynamics of Internal Layers and Diffusive Interfaces (SIAM, Philadelphia, PA, 1988).
24. H. Yamada and K. Nozaki, Physica D 64 (1993) 153.
25. V. Perez-Munuzuri, M. Gomez-Gesteira, A.P. Munuzuri, V.A. Davydov and V. Perez-Villar, Phys. Rev. E 51 (1995) R845.
26. P.K. Brazhnik, Physica D, submitted for publication.