Spectral Analysis for Optical Fibres and Stratified Fluids I: The Limiting Absorption Principle

@inproceedings{Debievre1991SpectralAF,
  title={Spectral Analysis for Optical Fibres and Stratified Fluids I: The Limiting Absorption Principle},
  author={Stephan Debievre and David W. Pravica},
  year={1991}
}
  • Stephan Debievre, David W. Pravica
  • Published 1991
  • Mathematics
  • The wave equation (∂t2+H)Ψ=0 withH=−c2(x,y)ρ(x,y)▽z·ρ(x,y)−1▽z, z=(x,y),xϵRk,yϵRm, describes the propagation of acoustical waves in stratified fluids (m = 1, k = 2), as well as electromagnetic waves in layered dielectric media (m = 1, k = 2), and in optical fibres (m = 2, k = 1,and p(x, y) = 1). The density p(x, y) and signal speed c(x, y) are (possibly long range) perturbations of a density p0(y) and speed c0(y), i.e., (p(x, y) − p0(y)), (c(x,y) − c0(y)) → 0 as ¦z¦→ ∞. Positive commutator… CONTINUE READING

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