Geodesic
Passage through the local resonance for a linear dispersive wave
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 113-123

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In this work we consider an inhomogeneous linear Schrodinger equation with rapidly oscillating right-hand side. We construct asymptotic solution to the small parameter in the presence of a local resonance. A complete asymptotic expansion of the solution is obtained using the matching method.
Keywords: small parameter, asymptotic solution, WKB approximation, resonance. 
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     author = {Z. R. Khakimova},
     title = {Passage through the local resonance for a linear dispersive wave},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {113--123},
     publisher = {mathdoc},
     number = {14},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a11/}
}
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Z. R. Khakimova. Passage through the local resonance for a linear dispersive wave. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 113-123. http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a11/