Abstract
The resonant interaction between collective modes in a quasi-one-dimensional (Q1D) attractive Bose–Einstein condensate (BEC) is considered. Nonlinearly coupled amplitude equations are derived using a method of multiple scales. Coupling matrix elements describing mode–mode resonances in both Landau and Beliaev mechanisms are calculated analytically. In particular, second-harmonic generation and three-mode resonant interaction of the collective modes in Q1D BEC are investigated in detail. The result shows that the physics of the resonant mode couplings in attractive Q1D BEC is richer than that of repulsive Q1D BEC.
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