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Recently energy exchange between two filaments crossing at small angle andwith power slightly above the critical for self-focusing $P_{cr}$ wasexperimentally demonstrated. In this paper we present a model describing theprocess of this transfer through degenerate four-photon parametric mixing. Ourmodel confirms the experimental results that the direction of energy exchangedepends on the relative transverse velocity (incident angle), laser intensityand initial distance between the pulses (relative initial phase). We alsoinvestigate the interaction between two collinear filaments in order to explainthe filaments number reduction for powers close to $P_{cr}$ in multi-filamentalpropagation.

Energy transfer between two filaments due to degenerate four-photon parametric process