Analytic singularities in dispersive wave phenomena based on topological singularities of dispersion relations

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Abstract
The connection between topological singularities of dispersion relations and analytic singularities with respect to frequency of spectral densities and wavefunctions in dispersive media due to time harmonic sources is demonstrated. The topological singularities are discussed within the framework of imperfect bifurcation theory, regarding the frequency as a distinguished bifurcation parameter and the wavenumbers as bifurcation variables, and using a recently obtained classification of topological singularities up to codimension four which is given in terms of a list of normal forms. To each normal form corresponds an analytic singularity, governed by characteristic exponents which are tabulated.

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