Collective-coordinate description of chaotic sine-Gordon breathers and zero-frequency breathers: The nondissipative case

Abstract

We study the onset of the temporal chaos in the ac-driven sine-Gordon system. A collective-coordinates theory is applied to reduce the original equation to an ordinary differential system for a single significant collective coordinate (the width of the nonlinear wave which is here assumed stationary). The Poincar\'e map of the reduced system allows one to study the regular and chaotic behavior for breathers and zero-frequency breathers. The presence of temporal horseshoe chaos, together with the survivance of spatial coherence, are predicted by means of the Melnikov theory and numerically checked. The resonant breathers are spatially preserved, but their chaotic temporal dynamic is described by the presence of islands in the Poincar\'e section of the reduced system. For increasing external ac field amplitudes, the Melnikov theory is no longer reliable. Therefore, we only perform numerical investigations in which we observe a more complicated chaotic behavior before the final breather breakup.