Abstract. Impacts on chains of identical beads can generate nonlinear waves such as solitary waves or fronts. We consider a long-wave regime that occurs when the exponent of the contact force approaches unity. In the absence of dissipation, solitary wave profiles can be approximated by a Gaussian solution to a logarithmic KdV equation. When a small contact damping is introduced, the analogous continuum limit corresponds to a logarithmic KdV-Burgers equation. This equation admits traveling front solutions which approximate compression fronts in the granular chain. We validate this approximation numerically, using both dynamical simulations (response of the chain to a compression by a piston) and the Newton method (computation of exact traveling waves by a shooting method).
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