Breathing self-localized solitons in the quartic Fermi-Pasta-Ulam chain

Abstract

If the fundamental self-localized soliton (SLS) of the Fermi-Pasta-Ulam chain is subjected to a perturbation of the same parity, a breathing behavior in space is observed. The time evolution then is characterized by two different frequencies. We show that the observed breathing behavior can be explained by means of a harmonic model with an effective spring hardening which is generated by the fundamental background SLS. The validity of this harmonic model is verified by means of numerical simulations. Improvements involving a parametric oscillator are mentioned but left to future study. \textcopyright{} 1996 The American Physical Society.