On the solitary wave pulse in a chain of beads
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- by J. M. English and R. L. Pego PDF
- Proc. Amer. Math. Soc. 133 (2005), 1763-1768 Request permission
Abstract:
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 $p^\textrm {th}$ power of the distance of approach of their centers with $p=\frac 32$. It is known that solitary wave solutions exist for such a system when $p>1$. 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.References
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Additional Information
- J. M. English
- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53705
- Email: english@math.wisc.edu
- R. L. Pego
- Affiliation: Department of Mathematics and Institute for Physical Sciences and Technology, University of Maryland, College Park, Maryland 20742
- Address at time of publication: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
- MR Author ID: 137455
- ORCID: 0000-0001-8502-2820
- Email: rlp@math.umd.edu, rpego@cmu.edu
- Received by editor(s): February 19, 2004
- Published electronically: January 14, 2005
- Additional Notes: This material is based upon work supported by the National Science Foundation under grants DMS 00-72609 and DMS 03-05985.
- Communicated by: Mark J. Ablowitz
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1763-1768
- MSC (2000): Primary 35B40, 35C15, 35Q51
- DOI: https://doi.org/10.1090/S0002-9939-05-07851-2
- MathSciNet review: 2120276