Abstract
We consider a cubic-quintic Gross–Pitaevskii equation which governs the dynamics of Bose–Einstein condensate matter waves with time-dependent scattering length and spatiotemporal complex potential. By introducing phase-imprint parameters in the system, we present the integrable condition for the equation and obtain the exact analytical solutions, which describe the propagation of a solitary wave. By applying specific time-modulated feeding/loss functional parameter, various types of magnetic trap strengths, and phase-imprint parameters, the dynamics of the solutions can be controlled. Solitary wave solutions with breathing and snaking behaviors are reported.
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