Abstract
Wave function of the Bose–Einstein condensate satisfies the nonlinear evolution equation set, which is composed of the driven-dissipative Gross–Pitaevskii equations and rate equation (GPR). In this paper, a three coupled GPR equation is studied. By virtue of the bilinear method, multi-soliton solutions of this GPR equation are attained. Propagation and interaction of the solitons are discussed: propagation direction of the solitons are determined by the wave number; repellent and attractive two solitons are obtained by virtue of adjustment the wave numbers; interaction of the two solitons bound state are discussed; three solitons bound state are attained.
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