Hierarchy of the Kadomtsev-Petviashvili equations under nonlocal constraints: Many-dimensional generalizations and exact solutions of reduced system |
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Authors: | A. M. Samoilenko V. G. Samoilenko Yu. M. Sidorenko |
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Affiliation: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev;(2) Shevchenko National University, Kiev |
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Abstract: | 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. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 78–97, January, 1999. |
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