Conversion of a pump wave into a pair of daughter waves resonantly coupled to it is studied analytically in an inhomogeneous medium in two cases: When the medium is slightly inhomogeneous, and when the resonant layer is very narrow, so that it may be approximated by the delta-function. In the former case, a configuration of the wave fields is sought for in a form close to the exact one-soliton solution of the homogeneous model. The evolution equations for parameters of the wave form are derived by means of the Langrangian formalism. In the latter case, the underlying equations of the resonant three-wave interaction can be integrated directly. In both cases, a share of the inital pump that does not decay into the daughters is found. In the former case this share is always small due to the underlying assumptions, while in the latter case it may be arbitrarily large.
|Number of pages||6|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - 5 Oct 1992|