  In our paper we construct a new infinite family of symmetries of the Whitham
equations (averaged Korteveg-de-Vries equation). In contrast with the ordinary
hydrodynamic-type flows these symmetries are nonhomogeneous (i.e. they act
nontrivially at the constant solutions), are nonlocal, explicitly depend upon
space and time coordinates and form a noncommutative algebra, isomorphic to the
algebra of the polynomial vector fields in the complex plane (Virasoro algebra
with the zero central charge).
