We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg–de Vries (KdV) equation in the special “condensate” limit. We prove that in this limit the integro-differential kinetic equation for the spectral density of states reduces to the
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Long-time approximations of small-amplitude, long-wavelength FPUT solutions
It is well known that the Korteweg-deVries(KdV) equation and its generalizations serve as modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation estimates and other such results have been proved in this case. However, situ- ations in which the defocusing modified KdV (mKdV) equation is expected to be the modulation equation have been much less studied. As seen in numerical experiments, the kink solution of the mKdV seems essential in understanding the -FPUT recurrence. In this paper, we derive explicit approximation re- sults for solutions of the FPUT using the mKdV as a modulation equation. In contrast to previous work, our estimates allow for solutions to be non-localized as to allow approximate kink solutions. These results allow us to conclude meta-stability results of kink-like solutions of the FPUT.
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- Award ID(s):
- 1813384
- NSF-PAR ID:
- 10478251
- Publisher / Repository:
- AIMS
- Date Published:
- Journal Name:
- Discrete and Continuous Dynamical Systems
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 1078-0947
- Page Range / eLocation ID:
- 0 to 0
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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