Non-compatible partially PT symmetric Davey-Stewartson system: rational solution in constant wave background

This paper derives a family of rational solutions with several non-zero offset parameters for a non-compatible partially PT symmetric Davey-Stewartson system by introducing small perturbation to the phase constant and using the “long wave” limit. This system models the evolution of optical wave packets in nonlinear optics, and provides two spatial dimensional analogue of the integrable nonlocal nonlinear Schrödinger equation(Phys Rev Lett 110:064105, 2013). In addition, the first two equations of such system are inconsistent that do not need to comply with extra constraints like the compatible system, which makes it more general and renders more possibilities. The obtained solutions consist of a single symmetric soliton or a few independent breathers. The existence of free parameters brings nontrivial changes to the higher order solutions as they are capable of decomposing into first order solutions. Our results not only perfectly retrieve the solutions obtained by the Darboux transformation for the focusing nonlinear Schrödinger equation(Phys Rev E 80:026601, 2009) but also extend it to the version containing free parameters. Our method is applicable to many nonlinear models that may be useful in simulating rogue waves in oceanic and optics.