Skip to main content
On the existence of solitary traveling waves for generalized Hertzian chains
Journal of Nonlinear Science (2011)
  • Panos Kevrekidis, UMASS, Amherst
  • Atanas Stefanov
We consider the question of existence of “bell-shaped” (i.e. non-increasing for x > 0 and non-decreasing for x < 0) traveling waves for the strain variable of the generalized Hertzian model describing, in the special case of a p = 3/2 exponent, the dynamics of a granular chain. The proof of existence of such waves is based on the English and Pego [Proceedings of the AMS 133, 1763 (2005)] formulation of the problem. More specifically, we construct an appropriate energy functional, for which we show that the constrained minimization problem over bell-shaped entries has a solution. We also provide an alternative proof of the Friesecke-Wattis result [Comm. Math. Phys 161, 394 (1994)], by using the same approach (but where the minimization is not constrained over bell-shaped curves). We briefly discuss and illustrate numerically the implications on the doubly exponential decay properties of the waves, as well as touch upon the modifications of these properties in the presence of a finite precompression force in the model.
Publication Date
Publisher Statement

DOI: 10.1007/s00332-011-9119-9

This is the pre-published version harvested from arXiv. The published version is located at
Citation Information
Panos Kevrekidis and Atanas Stefanov. "On the existence of solitary traveling waves for generalized Hertzian chains" Journal of Nonlinear Science Vol. 22 Iss. 3 (2011)
Available at: