Abstract

Short waves in a periodic potential on a periodic strip in two dimensions are studied in the parameter range where the spectrum has banded structure. The exponentially precise EBK theory of Parts I and II is applied to a restricted class of such wave problems to indicate why their continuous spectra can be complicated and how the spectral structure can be elucidated quantitatively. The results indicate the direction in which the analog for partial differential equations of the basic Floquet theorem for ordinary differential equations may be found.

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