Nonlinear Hertz contact forces between spheres create compact solitary waves with no dispersion
When spherical beads touch under Hertz contact mechanics, the compressive force obeys F = A·δ^(3/2) (for elastic spheres, n=3/2 generalized). This nonlinear interaction — unlike springs — creates compactly supported solitary waves: pulses that travel without spreading or changing shape, but NOT like KdV solitons (these don't pass through each other). Wave width is ~5 beads regardless of amplitude. Speed scales as v_s ∝ F^(1/6), confirmed by Nesterenko (1983) and Coste et al. (1997). Potential applications: acoustic diodes, shock absorbers, medical ultrasound.