Perturbation theory for periodic problems in 2D integrable systems

Krichever I.M.3718652188, 9783718652181

The perturbation theory of finite-zone solutions of two-dimensional integrable equations is developed. As a special case the theory of perturbations of finite-zone solutions of one-dimensional evolution equations of the Lax type (the Korteweg-de Vries and Sine-Gordon equations) is considered. The spectral theory of two-dimensional periodic operators is surveyed.