Open Access
2010 Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces
Vladimir S. Gerdjikov, Alexander V. Mikhailov, Tihomir I. Valchev
J. Geom. Symmetry Phys. 20: 1-34 (2010). DOI: 10.7546/jgsp-20-2010-1-34


We study certain classes of integrable nonlinear differential equations related to the type symmetric spaces. Our main examples concern equations related to A.III-type symmetric spaces. We use the Cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic Lax operators to this symmetric space. Next we outline the spectral theory of the reduced Lax operator $L$ and construct its fundamental analytic solutions. Analyzing the Wronskian relations we introduce the `squared solutions' of $L$ and derive the recursion operators by three different methods.


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Vladimir S. Gerdjikov. Alexander V. Mikhailov. Tihomir I. Valchev. "Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces." J. Geom. Symmetry Phys. 20 1 - 34, 2010.


Published: 2010
First available in Project Euclid: 25 May 2017

zbMATH: 1217.37065
MathSciNet: MR2780238
Digital Object Identifier: 10.7546/jgsp-20-2010-1-34

Rights: Copyright © 2010 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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