Quasigraded Lie Algebras and Modified Toda Field Equations
  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 $\mathfrak{g}$. 
Taras V. Skrypnyk