Compactons in strongly nonlinear lattices

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The goal of this project is the investigation of localized traveling objects - compactons - in strongly nonlinear lattices. Two particular examples - a chain of phase equations for coupled nonlinear oscillators and a one-dimensional chain of beads under Hertz contact - will be studied in details. We will find a traveling wave in a discrete lattice numerically and compare this solution with that of a quasi-continuum approximation.A perturbative approach for a nonideal lattices will be developed. Collisions of compactons, as well as the long-time properties like transition to chaos, will be investigated numerically.