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Journal article
Metastability of solitary waves in diatomic FPUT lattices
Mathematics in engineering, v 1(3), pp 419-433
01 Jan 2019
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Abstract
It is known that long waves in spatially periodic polymer Fermi-Pasta-Ulam-Tsingou lattices are well-approximated for long, but not infinite, times by suitably scaled solutions of Kortewegde Vries equations. It is also known that dimer FPUT lattices possess nanopteron solutions, i.e., traveling wave solutions which are the superposition of a KdV-like solitary wave and a very small amplitude ripple. Such solutions have infinite mechanical energy. In this article we investigate numerically what happens over very long time scales (longer than the time of validity for the KdV approximation) to solutions of diatomic FPUT which are initially suitably scaled (finite energy) KdV solitary waves. That is we omit the ripple. What we find is that the solitary wave continuously leaves behind a very small amplitude "oscillatory wake." This periodic tail saps energy from the solitary wave at a very slow (numerically sub-exponential) rate. We take this as evidence that the diatomic FPUT "solitary wave" is in fact quasi-stationary or metastable.
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Details
- Title
- Metastability of solitary waves in diatomic FPUT lattices
- Creators
- Nickolas Giardetti - Drexel Univ, Dept Math, 3141 Chestnut St, Philadelphia, PA 19104 USAAmy Shapiro - Drexel Univ, Dept Math, 3141 Chestnut St, Philadelphia, PA 19104 USAStephen Windle - Drexel Univ, Dept Math, 3141 Chestnut St, Philadelphia, PA 19104 USAJ. Douglas Wright - Drexel University
- Publication Details
- Mathematics in engineering, v 1(3), pp 419-433
- Publisher
- Amer Inst Mathematical Sciences-Aims
- Number of pages
- 15
- Grant note
- DMS-1511488 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000493713400002
- Scopus ID
- 2-s2.0-85181967566
- Other Identifier
- 991019182767704721
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- Web of Science research areas
- Mathematics, Interdisciplinary Applications