  The propagation of nonlinear waves in a lattice of repelling particles is
studied theoretically and experimentally. A simple experimental setup is
proposed, consisting in an array of coupled magnetic dipoles. By driving
harmonically the lattice at one boundary, we excite propagating waves and
demonstrate different regimes of mode conversion into higher harmonics,
strongly influenced by dispersion and discreteness. The phenomenon of acoustic
dilatation of the chain is also predicted and discussed. The results are
compared with the theoretical predictions of $\alpha$-FPU equation, describing
a chain of masses connected by nonlinear quadratic springs. The results can be
extrapolated to other systems described by this equation.
