ASA 124th Meeting New Orleans 1992 October

3aUW5. The existence of generalized eigenfunctions and multiple eigenvalues in underwater acoustics.

Richard B. Evans

Sci. Appl. Internatl. Corp., New London, CT 06320

An example is given of a horizontally stratified acoustic waveguide that supports generalized eigenfunctions in addition to the usual eigenfunctions or normal modes. Generalized eigenfunctions occur when the characteristic equation has a zero with multiplicity greater than one. Both eigenfunctions and generalized eigenfunctions are required to provide a complete representation of a wide class of functions. The separation of variables solution for a point source in a waveguide, based only on the usual eigenfunctions or normal modes, is not valid for the example presented here. The correct solution, based on a combination of eigenfunctions and generalized eigenfunctions, contains modes that are simultaneously exponentially damped and algebraically amplified in the direction of propagation.