Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV-type hierarchies is a quadruplet (A Λ, d1,d0), where the di are ℤ-gradations of a loop algebra A and Λ ∈ A is a semisimple element of the nonzero d1-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the d1-grade zero part of A into a vector space direct sum of two subalgebras This permits one to interpret certain Gelfand-Dickey-type systems associated with a nonstandard splitting of the algebra of pseudodifferential operators in the Drinfeld-Sokolov framework.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)