  Nonlinear interaction between normal modes dramatically affects energy
equipartition, heat conduction and other fundamental processes in extended
systems. In their celebrated experiment Fermi, Pasta and Ulam (FPU, 1955)
observed that in simple one-dimensional nonlinear atomic chains the energy must
not always be equally shared among the modes. Recently, it was shown that exact
and stable time-periodic orbits, coined $q$-breathers (QBs), localize the mode
energy in normal mode space in an exponential way, and account for many aspects
of the FPU problem. Here we take the problem into more physically important
cases of two- and three-dimensional acoustic lattices to find existence and
principally different features of QBs. By use of perturbation theory and
numerical calculations we obtain that the localization and stability of QBs is
enhanced with increasing system size in higher lattice dimensions opposite to
their one-dimensional analogues.
