Some stability properties of breathers in Hamiltonian networks of oscillators (Q1808340)

The author presents some stability properties of coupled anharmonic oscillators of the form \[ H(\{p_k,q_k\})= \sum_{k\in \mathbb{Z}} \Biggl( \frac{p_k^2+q_k^2}{2}+ \frac{1}{2N} q_k^{2N} \Biggr)+ \sum_{k\in \mathbb{Z}} \frac{1}{2} (q_k- q_{k-1})^2, \] where \(N\geq 6\) is a positive integer. The author shows that a relevant approximation of this model has breathers which are asymptotically stable in a suitable sense.