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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the solitary wave pulse in a chain of beads


Authors: J. M. English and R. L. Pego
Journal: Proc. Amer. Math. Soc. 133 (2005), 1763-1768
MSC (2000): Primary 35B40, 35C15, 35Q51
Published electronically: January 14, 2005
MathSciNet review: 2120276
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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 $p^{\rm th}$ power of the distance of approach of their centers with $p=\frac32$. 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.


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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
Email: rlp@math.umd.edu, rpego@cmu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07851-2
PII: S 0002-9939(05)07851-2
Keywords: Solitons, lattice, differential-difference equations, wave propagation
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.