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B-determining equations: applications to nonlinear partial differential equations

Published online by Cambridge University Press:  26 September 2008

O. V. Kaptsov
O. V. Kaptsov
Affiliation:
Computing Center, Academgorodok, 660036 Krasnoyrsk, Russia
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Abstract

We introduce the concept of B-determining equations of a system of partial differential equations that generalize the defining equations of the symmetry groups. We show how this concept may be applied to obtain exact solutions of partial differential equations. The exposition is reasonable self-contained, and supplemented by examples of direct physical importance, chosen from fluid mechanics.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 3 , June 1995 , pp. 265 - 286
Copyright
Copyright © Cambridge University Press 1995

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References

Bluman, G. W. & Cole, J. D. 1969 J. Math Mech. 18, 1025–1042.Google Scholar
Clarkson, P. & Kruskal, M. 1989 J. Math. Phys. 30, 2201–2213.CrossRefGoogle Scholar
Clarkson, P. & Hood, S. 1992 Euro. J. Appl. Math. 3, 381–415.CrossRefGoogle Scholar
Courant, R. & Hilbert, D. 1962 Methods of Mathematical Physics: Vol. 2: Partial Differential Equations. Wiley.Google Scholar
Courant, R. & Friedrichs, K. O. 1948 Supersonic Flow and Shock Waves. Wiley.Google Scholar
Hartman, Ph. 1964 Ordinary Differential Equations. Wiley.Google Scholar
Ibragimov, N. H. 1985 Transformation Groups Applied to Mathematical Physics. Reidel.CrossRefGoogle Scholar
Kaptsov, O. V. 1990 Prikl., Math. Mech. 54, 409–115 (in Russian).Google Scholar
Kaptsov, O. V. 1989 Din. Sploshoj Sredy 91, 37–47 (in Russian).Google Scholar
Levi-Civita, T. & Amaldi, U. 1927 Lezioni di Meccanica Razionale 2, 2.Google Scholar
Levi, D. & Winternitz, P. 1989 J. Phys. A: Math. Gen. 22, 2915–2924.CrossRefGoogle Scholar
Meleshko, S. V. 1983 Dokl. Acad. Nauk USSR 271, 42–46 (in Russian).Google Scholar
Olver, P. J. 1986 Applications of Lie Groups to Differential Equations. Springer-Verlag.CrossRefGoogle Scholar
Olver, P. J. & Rosenau, P. 1987 SIAM J. Appl. Math. 47, 263–278.CrossRefGoogle Scholar
Ovsiannikov, L. V. 1956 Dokl. Acad. Nauk USSR 118, 439–442 (in Russian).Google Scholar
Ovsiannikov, L. V. 1982 Group Analysis of Differential Equations. Academic Press.Google Scholar
Pommaret, J. F. 1978 Systems of Partial Differential Equations and Lie Pseudogroups. Gordon and Breach.Google Scholar
Riquier, C. H. 1910 Les systems ď equations aux derivees partielles. Gauthier-Villars.Google Scholar
Sidorov, A. F., Shapeev, V. P. & Yanenko, N. N. 1984 Method of differential constraints and its applications to gas dynamics. Nauka (in Russian).Google Scholar
Talishev, A. A. 1980 Chisl, Meth. Mech. Slosh. Sredy 11, 130–134 (in Russian).Google Scholar
Yanenko, N. N. 1991 Selected works. Nauka.Google Scholar