Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective

Authors
Publication date 2013
Journal Theoretical and Mathematical Physics
Volume | Issue number 174 | 1
Pages (from-to) 134-153
Organisations
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
Abstract We split the algebra of pseudodifferential operators in two different ways into the direct sum of two Lie subalgebras and deform the set of commuting elements in one subalgebra in the direction of the other component. The evolution of these deformed elements leads to two compatible systems of Lax equations that both have a minimal realization. We show that this Lax form is equivalent to a set of zero-curvature relations. We conclude by presenting linearizations of these systems, which form the key framework for constructing the solutions.

Document type Article
Note Also published in Russian: Helminck, G.F., Helminck, A.G. & Opimakh, A.V. (2010). Относительное расслоение реперов бесконечномерного многообразия флагов и решения интегрируемых иерархий. --- Теоретическая и математическая физика, 165 --- (3), 440-471.
Language English
Published at https://doi.org/10.1007/s11232-013-0011-7
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