Conditionally integrable PT -symmetric hierarchies and near-Lax pairs of the KdV and KPII equations

Earlier work is generalized to obtain novel conditionally-integrable hierarchies of various PT -symmetric, nonlinear partial differential equations. The Painleve Test yields the possible integrable cases. These are labeled by the integer n, the order of the dominant pole in the Laurent expansion for the solution. For the PT-symmetric Kortewegde Vries (KdV) equation which has been considered earlier, further analysis using the extended homogeneous balance technique gives the near-Lax Pair. Next, a PT-Symmetric hierarchy of (2 + 1) Kadomtsev-Petviashvili equations is considered. The Painleve Test and Invariant Painleve analysis in (2 + 1) dimensions yield special solutions and Backlund Transformations for the integrable cases.