Spectral theory for the periodic sine-Gordon equation: A concrete viewpoint

A summary of the spectral theory for quasiperiodic sine- and sinh-Gordon equations is given. Analogies with whole-line solitons and scattering theory motivates the discussion. The relation between the ingredients in the inverse spectral solution of the periodic sine-Gordon equation and physical characteristics of sine-Gordon waves is emphasized. The explicit topics covered are summarized in the table of contents in the Introduction.