Additional Reductions in the K -Constrained Modified KP Hierarchy

Abstract

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