Article contents
On nonclassical invertible transformations of hyperbolic equations
Published online by Cambridge University Press: 26 September 2008
Abstract
The main result of this paper is a complete description of local invertible transformations
relating one equation of the form uxy = F(x, y, u, ux, uy) to another equation of the form υxy = G(x, y, υ, υx, υy).
- Type
- Research Article
- Information
- Copyright
- Copyright © Cambridge University Press 1995
References
[1]Gardner, R. B. & Kamran, N. 1993 Characteristics and the Geometry of Hyperbolic Equations on the Plane. J. Differential Equations (to appear).Google Scholar
[2]Zhiber, A. V. & Shabat, A. B. 1984 Systems of equations ux = p(u, υ),υv = q(u, υ) having symmetries. Soviet Math. Dokl. 30 (1), 23–26.Google Scholar
[3]Leznov, A. N., Shabat, A. B. & Smirnov, V. G. 1982 The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems. Theor. Math. Phys. 51 (1), 322–330.CrossRefGoogle Scholar
[5]Vinogradov, A. M., Krasil'shchik, I. S. & Lychagin, V. V. 1986 Introduction into the Geometry of Nonlinear Differential Equations. Moscow: Nauka.Google Scholar
[6]Sokolov, V. V. 1988 On the symmetries of evolution equations. Russian Math. Surv. 43 (5), 165–204.Google Scholar
[7]Lund, F. 1978 Classically solvable field theory model. Ann. Phys. (USA) 115, 251–268.Google Scholar
[8]Anderson, I., Kamran, N. & Olver, P. J. 1993 Internal, external and generalized symmetries. Adv. in Math, (to appear).Google Scholar
[9]Olver, P. J. 1986 Applications of Lie groups to Differential Equations. Springer-Verlag.Google Scholar
[10]Zviagin, M. Y. 1990 Bivariate second order equations reducible to zxy = 0 via Baecklund transformations. Doklady AN SSSR 316(1), 36–40 (in Russian).Google Scholar
[12]Mikhailov, A. V., Shabat, A. B. & Sokolov, V. V. 1991 Symmetry Approach to Classification of Integrable Equations. What is integrability? Springer-Verlag, 115–184.Google Scholar
- 9
- Cited by