Differential equations

Passage through the local resonance for a linear dispersive wave

Z. R. Khakimova

Ufa State Petroleum Technological University

Abstract: 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.