Vekua theory for the Helmholtz operator
β Scribed by A. Moiola; R. Hiptmair; I. Perugia
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 480 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0044-2275
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## Abstract The paper is devoted to the investigation of the Helmholtz operators describing the propagation of acoustic waves in nonβhomogeneous space. We consider the operator __A__ with a wave number __k__ such that where __k__~0~ is a positive function, __k__~Β±~ are complex constants with βοΈ
We develop the theory of orthogonal R-separation for the Helmholtz equation on a pseudo-Riemannian manifold and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamiltonian-Jacobi equation. We provide a coordinate-free characterization of R-s