Granular Solitary Wave — Nesterenko Pulse

Solitary wave propagation in a granular chain via Hertz contact forces

Hertz Contact Law: The force between compressed beads scales as F = A·δn where δ is overlap and n = 3/2 for spheres (Hertz). This nonlinearity supports compact solitary waves (Nesterenko solitons) with no linear dispersion relation — unlike KdV solitons.
m·üi = A[δi−1,in − δi,i+1n]+
Wave speed scales as v ∝ A1/2, and the soliton width spans ~5 beads regardless of amplitude. A mass defect bead splits the pulse into reflected and transmitted waves.