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We investigate the macroscopic dynamics of sets of an arbitrary finite numberof weakly amplitude-modulated pulses in a multidimensional lattice ofparticles. The latter are assumed to exhibit scalar displacement underpairwise, arbitrary-range, nonlinear interaction potentials and are embedded ina nonlinear background field. By an appropriate multiscale ansatz, we deriveformally the explicit evolution equations for the macroscopic amplitudes up toan arbitrarily high order of the scaling parameter, thereby deducing theresonance and non-resonance conditions on the fixed wave vectors andfrequencies of the pulses, which are required for that. The derived equationsare justified rigorously in time intervals of macroscopic length. Finally, forsets up to three pulses we present a complete list of all possible interactionsand discuss their ramifications for the corresponding, explicitly givenmacroscopic systems.

Interaction of modulated pulses in scalar multidimensional nonlinear lattices