Translator Disclaimer
VOL. 12 | 2011 Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces
Vladimir Gerdjikov, Alexander Mikhailov, Tihomir Valchev

Editor(s) Ivaïlo M. Mladenov, Gaetano Vilasi, Akira Yoshioka

## 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.

## Information

Published: 1 January 2011
First available in Project Euclid: 13 July 2015

zbMATH: 1382.37075
MathSciNet: MR2780238

Digital Object Identifier: 10.7546/giq-12-2011-11-42