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- W4242711400 abstract "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." @default.
- W4242711400 created "2022-05-12" @default.
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- W4242711400 date "1992-10-01" @default.
- W4242711400 modified "2023-09-27" @default.
- W4242711400 title "The existence of generalized eigenfunctions and multiple eigenvalues in underwater acoustics" @default.
- W4242711400 doi "https://doi.org/10.1121/1.405254" @default.
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