Additional reductions in the k-constrained modified KP hierarchy

TL;DR

This paper introduces new reductions in the modified k-constrained KP hierarchy, leading to generalized integrable systems and a solution method using binary Darboux transformations.

Contribution

It proposes additional reductions in the hierarchy, resulting in generalized equations and a novel solution generating technique.

Findings

Generalizations of Kaup-Broer and KdV systems derived

Binary Darboux transformations developed for solutions

New integrable equations within the hierarchy identified

Abstract

Additional reductions in the modified k-constrained KP hierarchy are proposed. As a result we obtain generalizations of Kaup-Broer system, Korteweg-de Vries equation and a modification of Korteweg-de Vries equation that belongs to modified k-constrained KP hierarchy. We also propose solution generating technique based on binary Darboux transformations for the obtained equations.