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Abstract We study—experimentally, theoretically, and numerically—nonlinear excitations in lattices of magnets with long-range interactions. We examine breather solutions, which are spatially localized and periodic in time, in a chain with algebraically-decaying interactions. It was established two decades ago (Flach 1998Phys. Rev.E58R4116) that lattices with long-range interactions can have breather solutions in which the spatial decay of the tails has a crossover from exponential to algebraic decay. In this article, we revisit this problem in the setting of a chain of repelling magnets with a mass defect and verify, both numerically and experimentally, the existence of breathers with such a crossover.
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This content will become publicly available on July 1, 2025
Approximation of (some) random FPUT lattices by KdV equations
We consider a Fermi–Pasta–Ulam–Tsingou lattice with randomly varying coefficients. We discover a relatively simple condition which when placed on the nature of the randomness allows us to prove that small amplitude/long wavelength solutions are almost surely rigorously approximated by solutions of Korteweg–de Vries equations for very long times. The key ideas combine energy estimates with homogenization theory and the technical proof requires a novel application of autoregressive processes.
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- Award ID(s):
- 2006172
- PAR ID:
- 10560725
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Physica D: Nonlinear Phenomena
- Volume:
- 463
- Issue:
- C
- ISSN:
- 0167-2789
- Page Range / eLocation ID:
- 134154
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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