Dimensional Deformations of Integrable Systems: An Approach to Integrability in Multidimensions, Part 1

摘要

An approach, the dimensional deformations of integrable systems, to generate in a natural, straightforward and unified manner, higher dimensional analogs of integrable systems is proposed. In this approach, based on the theory describing the algebraic aspects of integrability, the algebraic structure of given integrable systems is explored, to generate integrable generalizations in higher dimensions. This approach is illustrated by examples and known and novel integrable systems are derived. The simplicity of the method allows also to single out the theoretical and technical problems responsible for the almost total absence of integrable structures in multidimensions.