Hierarchy of the Kadomtsev-Petviashvili equations under nonlocal constraints: Many-dimensional generalizations and exact solutions of reduced system - Samoilenko, A. M.; Samoilenko, V. G.; Sidorenko, Yu. M. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We present a spatially two-dimensional generalization of the hierarchy of Kadomtsev-Petviashvili equations under nonlocal constraints (the so-called 2-dimensionalk-constrained KP-hierarchy, briefly called the 2d k-c-hierarchy). As examples of (2+1)-dimensional nonlinear models belonging to the 2d k-c KP-hierarchy, both generalizations of already known systems and new nonlinear systems are presented. A method for the construction of exact solutions of equations belonging to the 2d k-c KP-hierarchy is proposed.