|
SIGMA 1 (2005), 023, 9 pages nlin.SI/0506027
https://doi.org/10.3842/SIGMA.2005.023
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
Abstract
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)
References
- Leznov A.N., Savel'ev M.V., Group methods of
integration of nonlinear dynamical systems, Moscow, Nauka, 1985 (in
Russian).
- Shabat A.B., Yamilov R.I., Exponential systems of type I
and the Cartan matrices, Preprint, Ufa, 1981.
- 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).
- Ward R.S., Discrete Toda field equations,
Phys. Lett. A, 1995, V.199, 45-48.
- 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).
- 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.
- Habibullin I.T., Characteristic algebras of the
discrete hyperbolic equations, nlin.SI/0506027.
- Habibullin I.T., Discrete Toda field
equations, nlin.SI/0503055.
|
|