Bounds on phase velocities of guided modes in open waveguides

Guiding of waves along cylinders with a surface impedance or along low velocity sound channels lead to eigenvalue problems in unbounded domains. Variational and comparison methods are used to find bounds on the discrete eigenvalues, which are related to the phase velocities of the guided modes. The variational methods yield upper bounds only, but they can be applied systematically to a large class of problems. The comparison methods yield upper and lower bounds, but are restricted to a smaller class of problems.