Reductions of Lower Triangular Toda Hierarchies


Helminck, Gerardus F. and Mishina, Marina G. and Polenkova, Svetlana V. (2007) Reductions of Lower Triangular Toda Hierarchies. Acta Applicandae Mathematicae, 99 (3). pp. 245-259. ISSN 0167-8019

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Abstract:Deforming commutative algebras in the lower triangular (ℤ×ℤ)-matrices yields lower triangular Toda hierarchies and their associated nonlinear equations. Like for their counterpart in the ring of pseudodifferential operators, the KP-hierarchy, one also has for these hierarchies a geometric picture: certain infinite chains of subspaces in an separable Hilbert space provide solutions of lower triangular Toda hierarchies. The KP-hierarchy and its multi-component version contain many interesting subsystems, like e.g. the nth Gelfand–Dickey hierarchy and the AKNS-hierarchy. In this paper one considers analogues of these two subsystems in the context of the lower triangular Toda hierarchies and a geometric description of solutions to both type reductions is given.
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Copyright:© 2007 Springer
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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