## Journal of Geometry and Symmetry in Physics

### Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces

#### Abstract

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.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 20 (2010), 1-34.

Dates
First available in Project Euclid: 25 May 2017

https://projecteuclid.org/euclid.jgsp/1495677844

Digital Object Identifier
doi:10.7546/jgsp-20-2010-1-34

Mathematical Reviews number (MathSciNet)
MR2780238

Zentralblatt MATH identifier
1217.37065

#### Citation

Gerdjikov, Vladimir S.; Mikhailov, Alexander V.; Valchev, Tihomir I. Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces. J. Geom. Symmetry Phys. 20 (2010), 1--34. doi:10.7546/jgsp-20-2010-1-34. https://projecteuclid.org/euclid.jgsp/1495677844