The recursion operator for a constrained CKP hierarchy

TL;DR

This paper introduces a recursion operator for a constrained CKP hierarchy and demonstrates its reduction to the mKdV hierarchy when specific conditions are met.

Contribution

It provides the first recursion operator for the 1-constrained CKP hierarchy and establishes its reduction to the mKdV hierarchy.

Findings

Recursion operator for 1-constrained CKP hierarchy derived.

Reduction to mKdV hierarchy under condition q=r.

The hierarchy's integrability properties are clarified.

Abstract

This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition $q=r$.