The Anti-FPU Problem

Details The Anti-FPU Problem The Anti-FPU Problem

2004-09-24

arxiv.org/abs/nlin/0409049v2

Chaos 15, 015110 (2005)

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1063/1.1854273

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.

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