Hierarchy of the Kadomtsev-Petviashvili equations under nonlocal constraints: Many-dimensional generalizations and exact solutions of reduced system

  • A. M. Samoilenko
  • V. G. Samoilenko
  • Yu. M. Sidorenko


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.
How to Cite
Samoilenko, A. M., V. G. Samoilenko, and Y. M. Sidorenko. “Hierarchy of the Kadomtsev-Petviashvili Equations under Nonlocal Constraints: Many-Dimensional Generalizations and Exact Solutions of Reduced System”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 51, no. 1, Jan. 1999, pp. 78–97, https://umj.imath.kiev.ua/index.php/umj/article/view/4585.
Research articles