The hidden algebraic structure of the Kaup-Broer hierarchy

Abstract

In this paper, we investigate the conformal algebra associated with the coupled Kaup-Broer hierarchy which is obtained from the coupled AKNS hierarchy by gauge transformation. We find that the algebraic structure hidden behind the coupled Kaup-Broer hierarchy can be revealed after mapping the Lax operator of the coupled Kaup-Broer hierarchy to a Yajima-Oikawa-type Lax operator. Furthermore, we show that the second Hamiltonian structure of the coupled Kaup-Broer hierarchy can be simplified by factorizing the Lax operator in multiplicative form and thus obtain the free-field realization of the associated algebras.