Communications in Partial Differential Equations · 1992 · 18 citations · 3 references
Natural SciencesPhysicsAcousticsFluid DynamicsOpticsAcoustic Wave PropagationEigenvalue ProblemsElectromagnetic WavesOptical FibersPropagation In Dielectric MediaSpectral TheoryAcoustic Properties Of FluidsCommutatorEigenvalue Problems In AcousticsEigenvalue Spectral AnalysisPoint SpectrumVirial TheoremWave Dynamics In Stratified FlowWave Propagation In Stratified Fluids
Abstract The operator Ĥ appears in the study of the propagation of acoustical waves in stratified fluids , as well as of electromagnetic waves in layered dielectric media , and in optical fibres . The density and signal speed are (possibly long range) perturbations of a density and speed , . Positive commutator methods along with Virial techniques are used to show that in many cases of physical interest the point spectrum of Ĥ is empty. More generally, eigenfunctions of Ĥ if they exist, must decay faster than .
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