The homogeneous realization of the basic representation of \(A_ 1^{(1)}\) and the Toda lattice
The principal realization of the basic module \(L(\Lambda_ 0)\) over \(A_ 1(1)\) is known to give rise to the KdV hierarchy of partial differential equations. The authors use the homogeneous realization of the same module to construct a hierarchy of differential-difference equations, the first term of which turns out to be the equation for the Toda lattice. Thus, both hierarchies describe the same abstract orbit in \(L(\Lambda_ 0)\). In particular, the n-soliton solution of the KdV corresponds to a solution of the 2n-particle Toda lattice.
hierarchy of differential- difference equations
scientific article; zbMATH DE number 3993813