Reductions of Darboux transformations for the PT-symmetric nonlocal Davey-Stewartson equations

In this letter, a study of the reductions of the Darboux transformations (DTs) for the PT-symmetric nonlocal Davey-Stewartson (DS) equations is presented. Firstly, a binary DT is constructed in integral form for the PT-symmetric nonlocal DS-I equation. Secondly, an elementary DT is constructed in differential form for the PT-symmetric nonlocal DS-II equation. Afterwards, a new binary DT in integral form is also found for the nonlocal DS-II equation. Moreover, it is shown that the symmetry properties in the corresponding Lax-pairs of the equations are well preserved through these DTs. Thirdly, based on above DTs, the fundamental rogue waves and rational travelling waves are obtained.