  We calculated the spectrum of normal scalar waves in a planar waveguide with
absolutely soft randomly rough boundaries beyond the perturbation theories in
the roughness heights and slopes, basing on the exact boundary scattering
potential. The spectrum is proved to be a nearly real non-analytic function of
the dispersion $\zeta^2$ of the roughness heights (with square-root
singularity) as $\zeta^2 \to 0$. The opposite case of large boundary defects is
summarized.
