## Geometry of the recursion operators for Caudrey-Beals-Coifman system in the presence of Mikhailov type $$\mathbb Z_p$$ reductions.(English)Zbl 1329.35264

Summary: We give a geometric picture for the recursion operators related to the Caudrey-Beals-Coifman linear problem and the nonlinear evolution equations associated to it in the presence of $$\mathbb Z_p$$ reductions of Mikhailov type.

### MSC:

 35Q51 Soliton equations 37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems