KdV-Type Equations and W-Algebras

Abstract

This chapter focuses on KdV-type equations and W-algebras. There exists a remarkable connection between the conformal field theory and the theory of KdV-type equations. The symmetry generators in conformal field theory form an associative infinite-dimensional algebra which always contains the Virasoro algebra as a subalgebra. A very interesting class of conformal algebras was considered first by A. B. Zamolodchikov. It is the so called W-algebras. The first example of a W-algebra is the Virasoro algebra itself. W-algebra can also be considered as quantum version of a certain structure in the theory of KdV-type equations.