Abstract
Based on the inhomogeneous cubic–quintic nonlinear Schrodinger equation with external real or complex potential, we investigate in this chapter the dynamics of Bose–Einstein condensates when both the two- and three-body interatomic interactions are taken into consideration. We start by performing different methods leading to the exact analytical periodic and solitary wave solutions of such equations. Via these exact solutions, we investigate quantitatively and qualitatively the dynamical properties including the coherent structures and the modulational instability of matter waves in BECs with both the two- and three-body interactions. The effects of the three-body interaction in weakly interacting BECs are also investigated.
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