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Journal article
Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
Physica. D, v 358
01 Nov 2017
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Abstract
Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size. In particular we address the limit where the mass ratio tends to zero. The problem is inherently singular and we find that the traveling waves are not true solitary waves but rather "nanopterons", which is to say, waves which are asymptotic at spatial infinity to very small amplitude periodic waves. Moreover, we can only find solutions when the mass ratio lies in a certain open set. The difficulties in the problem all revolve around understanding Jost solutions of a nonlocal Schrodinger operator in its semi-classical limit. (C) 2017 Elsevier B.V. All rights reserved.
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Details
- Title
- Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
- Creators
- Aaron Hoffman - Franklin W. Olin College of EngineeringJ. Douglas Wright - Drexel University
- Publication Details
- Physica. D, v 358
- Publisher
- Elsevier
- Number of pages
- 27
- Grant note
- 1511488 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS) DMS-1105635; DMS-1511488 / National Science Foundation; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000412259600004
- Scopus ID
- 2-s2.0-85027677840
- Other Identifier
- 991019182651304721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Fluids & Plasmas
- Physics, Mathematical
- Physics, Multidisciplinary