$$\overline{\partial }$$-dressing method to PT-symmetric multi-component nonlinear Schrödinger equation

Abstract

In this paper, the PT-symmetric multi-component nonlinear Schrödinger (PTSMCNLS) equation is derived using the ∂-dressing method in two local 4 × 4 matrix ∂-problems. The relations between the potential of the PTSMCNLS equation and the solution of the ∂-problem are established. The explicit Nsoliton solutions of the PTSMCNLS equation are obtained. Moreover, the PT-symmetric three-component nonlinear Schrödinger (PTSTCNLS) equation is constructed by virtue of reduction. As applications, some specific soliton dynamical behaviors are theoretically explored and graphically illustrated.