On the solitary wave pulse in a chain of beads

We study the shape of solitary wave pulses that propagate in an infinite chain of beads initially in contact with no compression. For this system, the repulsive force between two adjacent beads is proportional to the p th p^th power of the distance of approach of their centers with p = 3 2 p= 32 . It is known that solitary wave solutions exist for such a system when p > 1 p>1 . We prove extremely fast, double-exponential, asymptotic decay for these wave pulses. An iterative method of solution is also proposed and is seen to work well numerically.