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.