Graded Lie algebras, representation theory, integrable mappings and systems
A. N. Leznov
Abstract
A new class of integrable mappings and chains is introduced. Corresponding (1+2) integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in terms of matrix elements of fundamental representations of semisimple An algebras for a given group element. The possibility of generalizing this construction to multi-dimensional case is discussed.
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