  We review and slightly improve the known k-polysymplectic Marsden--Weinstein
reduction theory by removing some technical conditions on k-polysymplectic
momentum maps by developing a theory of affine Lie group actions for
k-polysymplectic momentum maps, removing the necessity of their co-adjoint
equivariance. Then, we focus on the analysis of a particular case of
k-polysymplectic manifolds, the so-called fibred ones, and we study their
k-polysymplectic Marsden--Weinstein reductions. Previous results allow us to
devise a k-polycosymplectic Marsden--Weinstein reduction theory, which
represents one of our main results. Our findings are applied to study coupled
vibrating strings and, more generally, k-polycosymplectic Hamiltonian systems
with field symmetries. We show that k-polycosymplectic geometry can be
understood as a particular type of k-polysymplectic geometry. Finally, a
k-cosymplectic to l-cosymplectic geometric reduction theory is presented, which
reduces, geometrically, the space-time variables in a k-cosymplectic framework.
An application of this latter result to a vibrating membrane with symmetries is
given.
