Abstract: I define higher versions of contact structures on manifolds as maximally non-integrable distributions. I call them multicontact structures. Cartan
distributions on jet spaces provide canonical examples. More generally, I define higher versions
of pre-contact structures
as distributions on manifolds
whose characteristic symmetries span a constant dimensional distribution. Every distribution is almost everywhere, locally, a pre-multicontact structure. After showing that the standard symplectization of contact manifolds generalizes naturally to a (pre-)multisymplectization of (pre)multicontact manifolds, I make use of results
by C. Rogers and M. Zambon to associate
a canonical L-infinity algebra
to any (pre-)multicontact structure. Such L-infinity algebra is a higher version of the Jacobi
brackets on contact manifolds. Since every partial differential
equation (PDE) can be geometrically understood as a manifold with a distribution, then there is
a (contact invariant) L-infinity algebra attached to any PDE. Finally, I describe in local coordinates the L-infinity
algebra associated with the Cartan
distribution on jet spaces.