A Coset-Construction for Integrable Hierarchies
The principal realization of the basic representation of an affine Kac-Moody algebra can be applied to construct soliton solutions of hierarchies of partial differential equations, among them the KdV- and KP-equations.
In this construction, called orbit-construction, the equations of the hierarchy itself arise in Hirota bilinear form. Using the Goddard-Kent-Olive coset-construction of conformai field theory, we show that the equations are generated by a pair of commuting c=1/2 Virasoro algebras in the KdV-case. We end with a brief discussion of other cases.
KeywordsTensor Product Soliton Solution Conformal Field Theory Classical Hierarchy High Weight Vector
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