Coherence and chaos in the driven damped sine-Gordon equation: measurement of the soliton spectrum
A numerical procedure is developed which measures the sine-Gordon soliton and radiation content of any field \((\phi,\phi_ t)\) which is periodic in space. The procedure is applied to the field generated by a damped, driven sine-Gordon equation. This field can be either temporally periodic (locked to the driver) or chaotic. In either case the numerical measurement shows that the spatial structure can be described by only a few spatially localized (soliton wave-train) modes. The numerical procedure quantitatively identifies the presence, number and properties of these soliton wave-trains. For example, an increase of spatial symmetry is accompanied by the injection of additional solitons into the field.
scientific article; zbMATH DE number 3996263