The method of contact integrable extensions is used to find new differential coverings for the generalized (2 + 1)-dimensional dispersionless Dym equation and corresponding Bäcklund transformations.
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.
Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).
Equations with several brackets arose originally in the works of Brockett [2], [3] (for ordinary differential equations) and Felipe [5] (for partial differential equations) of double bracket equations of Lax type. The purpose of this note is to study triple bracket equations of the form:∂L / ∂t = [L,[L,[L,P]]]. deal with some algebraic properties of these equations, in particular we show that, as in the classical case, they are related to the presence of an infinite sequence of first integrals....