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- Title
The Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides.
- Authors
Anikin, A.; Dobrokhotov, S.; Nazaikinskii, V.; Rouleux, M.
- Abstract
The problem of constructing the asymptotics of the Green function for the Helmholtz operator h Δ + n ( x), x ∈ R , with a small positive parameter h and smooth n ( x) has been studied by many authors; see, e.g., [1, 2, 4]. In the case of variable coefficients, the asymptotics was constructed by matching the asymptotics of the Green function for the equation with frozen coefficients and a WKB-type asymptotics or, in a more general situation, the Maslov canonical operator. The paper presents a different method for evaluating the Green function, which does not suppose the knowledge of the exact Green function for the operator with frozen variables. This approach applies to a larger class of operators, even when the right-hand side is a smooth localized function rather than a δ-function. In particular, the method works for the linearized water wave equations.
- Subjects
MASLOV index; LAGRANGIAN functions; VECTOR spaces; HELMHOLTZ equation; WAVE equation
- Publication
Doklady Mathematics, 2017, Vol 96, Issue 1, p406
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562417040275