Lifetime and decay of seeded breathers in the FPU system

The Fermi-Pasta-Ulam problem [1] consists of a chain of N oscillators with linear and nonlinear nearest neighbor interactions. Using velocity-Verlet integration, we study the evolution of the system after a perturbation that consists of a single stretched bond at the center of the chain [2-4]. This perturbation results in the localization of most of the system's energy in the center particles in the form of a ``breather'' up to reasonably long times, which leaks energy at a rate depending on the potential parameters and the perturbation amplitude. The breather eventually undergoes a catastrophic breakdown, releasing all of its energy into acoustic noise and solitary waves. We explore the conditions on the amplitude and the parameters $\alpha $, $\beta $ for which a seeded breather will be most or least stable. Also we show how the overlap or lack thereof between the breather's primary frequencies and the acoustic frequencies influences its long-time stability. \\[4pt] [1] E. Fermi, J. Pasta, and S. Ulam, Los Alamos Scientific Laboratory Report No. LA-1940 (1955).\\[0pt] [2] S. Flach and A. V. Gorbach, Phys. Rep. \textbf{467}, 1 (2008).\\[0pt] [3] A. J. Sievers and S. Takeno, Phys. Rev. Lett. \textbf{61}, 970 (1988).\\[0pt] [4] T. K. Mohan and S. Sen, Pramana \textbf{77}, 975 (2011).