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We theoretically investigate the dynamics of two dark solitons in a polaritoncondensate under nonresonant pumping, based on driven dissipativeGross-Pitaevskii equations coupled to the rate equation. In particular, theanalytical expression of the effective potential between two dark solitons isgiven. The resulting equation of motion captures how the open-dissipativecharacter of a polariton Bose-Einstein condensate affects the properties ofdynamics of two-dark soliton, i.e., two-dark soliton relax by blending with thebackground at a finite time. We further simulate the relative motion of twodark solitons numerically with the emphasis on how two solitons' motion beingmanipulated the initial velocity, which are in excellent agreement with theanalytical results. The prediction of this work is sufficient for theexperimental observations within current facilities.

Dynamics of two dark solitons in a polariton condensate under non-resonant pumping