partial derivative<overline>-dressing method to PT-symmetric multi-component nonlinear Schrödinger equation

PT-symmetry is physically useful as it can overcome losses while still preserving guidance properties of the system. In this paper, the PT-symmetric multi-component nonlinear Schr & ouml;dinger (PTSMCNLS) equation is derived using the partial derivative<overline>-dressing method in two local 4 x 4 matrix partial derivative<overline>-problems. The relations between the potential of the PTSMCNLS equation and the solution of the partial derivative<overline>-problem are established. The explicit N-soliton solutions of the PTSMCNLS equation are obtained. Moreover, the PT-symmetric three component nonlinear Schr & ouml;dinger (PTSTCNLS) equation is constructed by virtue of reduction. As applications, some specific soliton dynamical behaviors are theoretically explored and graphically illustrated.