| Abstract: |
| In this talk, we are concerned with a nonlocal coupled nonlinear Schr\{o}dinger (NLCNLS) equation with PT-symmetry for mixed zero and nonzero boundary conditions. By combining the Hirota`s bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method, general {mixed-type soliton solution} to the NLCNLS equation with PT-symmetry {is constructed}. To be specific, we start with a set of bilinear equations satisfied by the tau functions of the two-component KP hierarchy with shifted singular points, $N$-bright-dark soliton solution is derived from a series of reductions such as complex conjugate and PT-symmetry reductions. It is quite interesting that, quite different from the nonlocal NLS equation with PT-symmetry, a nonsingular moving bright soliton solution exists in one-component while the the other component possessing a dark soliton solution. |
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