Quasigraded Lie Algebras and Modified Toda Field Equations - Skrypnyk, T.V. (Symmetry, Integrability and Geometry: Methods and Applications, 2006)
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 g.