Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric potential

A two component nonlocal vector nonlinear Schrödinger equation (VNLSE) is considered with a self-induced parity-time-symmetric potential. It is shown that the system possess a Lax pair and an infinite number of conserved quantities and hence integrable. Some of the conserved quantities like number operator, Hamiltonian etc. are found to be real-valued, in spite of the corresponding charge densities being complex. The soliton solution for the same equation is obtained through the method of inverse scattering transformation and the condition of reduction from nonlocal to local case is mentioned.