  We propose a classical analogue of the vertex algebra in the context of
classical integrable field theories. We use this fundamental notion to describe
the auxiliary function of the linear auxiliary problem as a classical vertex
operator. Then using the underlying algebra satisfied by the auxiliary function
together with the linear auxiliary problem we identify the local integrals of
motion, which by construction are in involution. The time components of the Lax
pair are also identified in terms of the classical vertex operators. Systems in
the presence of point like defects as well as systems on the semi-infinite line
are investigated. Specific examples associated to the classical Yangian and
twisted Yangian are also presented.
