Taras V. Skrypnyk, “Quasigraded Lie Algebras and Modified Toda Field Equations”, SIGMA, 2006, Volume 2,043, 14 pp.

This article is cited in 5 papers

Quasigraded Lie Algebras and Modified Toda Field Equations

Taras V. Skrypnyk^ab

^a Bogolyubov Institute for Theoretical Physics, 14-b Metrologichna Str., Kyiv, 03143 Ukraine
^b Institute of Mathematics, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine

Abstract: We construct a family of quasigraded Lie algebras that coincide with the deformations of the loop algebras in “principal” gradation and admit Kostant–Adler–Symes scheme. Using them we obtain new Volterra coupled systems and modified Toda field equations for all series of classical matrix Lie algebras $\mathfrak g$.

Keywords: infinite-dimensional Lie algebras; soliton equations.

MSC: 37K05; 37K30

Received: October 31, 2005; in final form March 3, 2006; Published online April 16, 2006

Language: English

DOI: 10.3842/SIGMA.2006.043