CHAOTIC AND PHASE-LOCKED BREATHER DYNAMICS IN THE DAMPED AND PARAMETRICALLY DRIVEN SINE-GORDON EQUATION

The dynamics of a breather in the damped and parametrically driven sin e-Gordon equation is investigated both numerically and analytically. T he Kahunen-Loeve expansion is applied to extract the energetically dom inant localized modes. These modes are used in a Galerkin approximatio n to the original partial differential equation. The solutions of the resulting amplitude equations are then compared to numerical simulatio ns of the perturbed sine-Gordon equation showing a perfect agreement. In addition, two collective-coordinate models (based on a direct appro ach and on the inverse-scattering transform) are constructed and their limitations in comparison with the Kahunen-Loeve expansion and direct simulations are discussed. Finally, information from the periodic spe ctral theory and linear stability analysis is used to identify the Kah unen-Loeve modes and to show why this approach gives rather good resul ts.