Rational soliton solutions in the parity-time-symmetric nonlocal coupled nonlinear Schrödinger equations

Abstract

In this paper, via the Darboux transformation (DT) method, we study the nonlocal coupled nonlinear Schrödinger (NLS) equations with parity-time (PT)-symmetric nonlinearities. We construct the N-fold iterative generalized DT and derive rational vector soliton solutions from a non-vanishing background. The first-order rational solution in each component can exhibit elastic interactions of antidark-antidark, dark-antidark, and antidark-dark rational solitons whose dynamics are the same as ones in nonlocal scalar NLS equation. The second-order rational solution possesses abundant interaction patterns. They not only can display elastic interaction between two rational solitons with combined-peak-valley profiles, but also can exhibit the dynamics of localized nonlinear excitation for rational antidark solitons generating high and steep hump wave patterns in the region of the interaction. We expect that the results in this work will be useful to study rational solitons in coupled PT-symmetric optical waveguides.