  We construct explicitly a class of coboundary Poisson-Lie structures on the
group of formal diffeomorphisms of ${\Bbb R}^n$. Equivalently, these give rise
to a class of coboundary triangular Lie bialgebra structures on the Lie algebra
$W_n$ of formal vector fields on ${\Bbb R}^n$. We conjecture that this class
accounts for all such coboundary structures. The natural action of the
constructed Poisson-Lie diffeomorphism groups induces large classes of
compatible Poisson structures on ${\Bbb R}^n$, thus making it a Poisson
homogeneous space. Moreover, the left-right action of the Poisson-Lie groups
$FDiff({\Bbb R}^m)\times FDiff({\Bbb R}^n)$ induces classes of compatible
Poisson structures on the space $J^{\infty}({\Bbb R}^m,{\Bbb R}^n)$ of infinite
jets of smooth maps ${\Bbb R}^m\to {\Bbb R}^n$, which makes it also a Poisson
homogeneous space for this action. Initial steps towards classification of
these structures are taken.
