- Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective
- Theoretical and Mathematical Physics
- Volume | Issue number
- 174 | 1
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
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.
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- 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.
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