  In this letter we consider the nonlinear realizations of the classical
Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant
reduction procedure allow us to deduce the Boussinesq equation with
interchanged space and evolution coordinates. By adding one more space
coordinate and introducing two copies of the $W_3^{(2)}$ algebra, the same
method yields the $sl(3,R)$ Toda lattice equations.
