Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 1 (2005), 023, 9 pages      nlin.SI/0506027

Characteristic Algebras of Fully Discrete Hyperbolic Type Equations

Ismagil T. Habibullin
Institute of Mathematics, Ufa Scientific Center, Russian Academy of Sciences, 112 Chernyshevski Str., Ufa, 450077 Russia

Received August 04, 2005, in final form November 30, 2005; Published online December 02, 2005

The notion of the characteristic Lie algebra of the discrete hyperbolic type equation is introduced. An effective algorithm to compute the algebra for the equation given is suggested. Examples and further applications are discussed.

Key words: discrete equations; invariant; Lie algebra; exact solution; Liuoville type equation.

pdf (187 kb)   ps (148 kb)   tex (11 kb)


  1. Leznov A.N., Savel'ev M.V., Group methods of integration of nonlinear dynamical systems, Moscow, Nauka, 1985 (in Russian).
  2. Shabat A.B., Yamilov R.I., Exponential systems of type I and the Cartan matrices, Preprint, Ufa, 1981.
  3. Zabrodin A.V., The Hirota equation and the Bethe ansatz, Teoret. Mat. Fiz., 1998, V.116, N 1, 54-100 (English transl.: Theoret. and Math. Phys., 1998, V.116, N 1, 782-819).
  4. Ward R.S., Discrete Toda field equations, Phys. Lett. A, 1995, V.199, 45-48.
  5. Adler V.E., Startsev S.Ya., On discrete analogues of the Liouville equation, Teoret. Mat. Fiz., 1999, V.121, N 2, 271-284 (English transl.: Theoret. and Math. Phys., 1999, V.121, N 2, 1484-1495).
  6. Hirota R., The Bäcklund and inverse scattering transform of the K-dV equation with nonuniformities, J. Phys. Soc. Japan, 1979, V.46, N 5, 1681-1682.
  7. Habibullin I.T., Characteristic algebras of the discrete hyperbolic equations, nlin.SI/0506027.
  8. Habibullin I.T., Discrete Toda field equations, nlin.SI/0503055.

Previous article   Next article   Contents of Volume 1 (2005)