On symmetries of integro-differential equations

• Autorzy: Zawistowski Z.J.
• Języki publikacji: EN

Abstrakty

EN

A new, general method is presented for the determination of Lie symmetry groups of integro-differential equations. The exhibited method is a natural extension of the famous Ovsiannikov method developed for differential equations. The method leads to significant applications for instance to the Vlasov-Maxwell equations, which are integro-differential type irreducible to differential equations.

Słowa kluczowe

EN

Lie groups; symetry; integro-differential equations; Vlasov plasmas

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 1998
• Tom: Vol. 46, nr 2
• Strony: 187--197
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Zawistowski Z.J.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland.

Bibliografia

• [1] Z. J. Zawistowski, Application of group theory to integro-differential equations of plasma physics [in Polish), IFTR Reports, No 23, 1992 and Ph.D. Thesis [in Polish), IPPT PAN, Warszawa 1997.
• [2] L. V. Ovsiannikov, Group analysis of differential equations, Academic Press, Boston 1982.
• [3] N. Ch. Ibragimov, Transformation groups applied to mathematical physics, Reidel, Dordrecht 1985.
• [4] P. J. Olver, Applications of Lie groups to differential equations, Springer Verlag, New York 1986.
• [5] G. W. Bluman, S. Kumei, Symmetries and differential equations, Springer-Verlag, New York 1989.
• [6] H. Stephani, Differential equations. Their solutions using symmetries, ed.: M. McCallum, Cambridge University Press, Cambridge 1989.
• [7] W. B. Taranov, On symmetries of one-dimensional, high frequency plasma moovements [in Russian], ZTF, 46 (1976) 1271-1277.
• [8] A. M. Vinogradov, I. S. Krasilshchik, Nonlocal symmetries and the theory of covering, Acta Applicandae Mathematicae, 2 (1984) 79-96.
• [9] R. T. Glassey, The Cauchy problem in kinetic theory SIAM, Philadelphia 1992.
• [10] I. M. Gelfand, S. W. Fomin, Calculus of variations, Prentice-Hall, Englewood Cliff 1962.
• [11] Z. J. Zawistowski, A. J. Turski, Symmetries of nonlocal Schrödinger Equation for Langmuir waves in Vlasov plasmas, (in printing in) J. Tech. Phys., (No 3, 1998).