Geodesic
Characteristic Algebras of Fully Discrete Hyperbolic Type Equations
Symmetry, integrability and geometry: methods and applications, Tome 1 (2005) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Mots-clés : discrete equations; invariant; Lie algebra; exact solution; Liuoville type equation. 
@article{SIGMA_2005_1_a22,
     author = {Ismagil T. Habibullin},
     title = {Characteristic {Algebras} of {Fully} {Discrete} {Hyperbolic} {Type} {Equations}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2005},
     volume = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a22/}
}
TY  - JOUR
AU  - Ismagil T. Habibullin
TI  - Characteristic Algebras of Fully Discrete Hyperbolic Type Equations
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2005
VL  - 1
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a22/
LA  - en
ID  - SIGMA_2005_1_a22
ER  - 
%0 Journal Article
%A Ismagil T. Habibullin
%T Characteristic Algebras of Fully Discrete Hyperbolic Type Equations
%J Symmetry, integrability and geometry: methods and applications
%D 2005
%V 1
%U http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a22/
%G en
%F SIGMA_2005_1_a22
Ismagil T. Habibullin. Characteristic Algebras of Fully Discrete Hyperbolic Type Equations. Symmetry, integrability and geometry: methods and applications, Tome 1 (2005). http://geodesic.mathdoc.fr/item/SIGMA_2005_1_a22/

[1] Leznov A. N., Savel'ev M. V., Group methods of integration of nonlinear dynamical systems, Nauka, Moscow, 1985 (in Russian) | MR | Zbl

[2] Shabat A. B., Yamilov R. I., Exponential systems of type I and the Cartan matrices, Preprint, Ufa, 1981

[3] Theoret. and Math. Phys., 116:1 (1998), 782–819 | DOI | MR | Zbl

[4] Ward R. S., “Discrete Toda field equations”, Phys. Lett. A, 199 (1995), 45–48 | DOI | MR | Zbl

[5] Theoret. and Math. Phys., 121:2 (1999), 1484–1495 | DOI | MR | Zbl

[6] Hirota R., “The Bäcklund and inverse scattering transform of the KdV equation with nonuniformities”, J. Phys. Soc. Japan, 46:5 (1979), 1681–1682 | DOI | MR

[7] Habibullin I. T., Characteristic algebras of the discrete hyperbolic equations, arXiv:nlin.SI/0506027

[8] Habibullin I. T., Discrete Toda field equations, arXiv:nlin.SI/0503055