Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-21T12:45:39.606Z Has data issue: false hasContentIssue false
  • English
  • Français

On nonclassical invertible transformations of hyperbolic equations

Published online by Cambridge University Press:  26 September 2008

V. V. Sokolov  and
S. I. Svinolupov
V. V. Sokolov
Affiliation:
Mathematical Institute of Ufa, Center of Russian Academy of Sciences, Chernyshevsky str. 112, 450000, Russia
S. I. Svinolupov
Affiliation:
Mathematical Institute of Ufa, Center of Russian Academy of Sciences, Chernyshevsky str. 112, 450000, Russia
Get access Rights & Permissions [Opens in a new window]

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
European Journal of Applied Mathematics , Volume 6 , Issue 2 , April 1995 , pp. 145 - 156
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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
[4]Ovsiannikov, L. V. 1978 Group Analysis of Differential Equations. Moscow: Nauka.Google 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
[11]Loewner, C.J. Anal. Math. 1952–1953, 2, 219.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