A quasi-periodic route to chaos in a near-integrable pde

Pattern formation and transitions to chaos are described for the damped, ac-driven, one-dimensional, periodic sine-Gordon equation. In a nonlinear Schrödinger regime, a generic quasi-periodic route to intermittent chaos is exhibited in detail using a range of dynamical systems diagnostics. In addition, a nonlinear spectral transform is exploited: (i) to identify and quantify coordinates of space-time attractors in terms of a small number of soliton modes of the underlying integrable system; (ii) to use these analytic coordinates to identify homoclinic orbits as possible sources of chaos; and (iii) to demonstrate the significance of energy transfer between coherent and extended states in this chaotic system.