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