Trapped surface waves in a periodic layer of a heavy liquid

The spectrum of a periodic waveguide with immersed and semi-immersed cylindrical bodies, the axes of which are parallel to the generatrix of the periodic relief of the bottom, is investigaged within the limits of the linearized theory of waves on the surface of a heavy liquid. Simple sufficient conditions for the existence of localized solutions are discovered in the case of a wave travelling at an acute angle to the generatrix. The numerous consequences of the result are discussed and a periodic waveguide is constructed, in the intrinsic spectrum of which there is a lacuna.