A new (1+1)-dimensional matrix k-constrained KP hierarchy

We introduce a new generalization of matrix (1+1)-dimensional k-constrained KP hierarchy. The new hierarchy contains matrix generalizations of stationary DS systems, (2+1)-dimensional modified Korteweg-de Vries equation and the Nizhnik equation. A binary Darboux transformation method is proposed for integration of systems from this hierarchy.

💡 Research Summary

The paper presents a novel extension of the (1+1)-dimensional matrix k‑constrained Kadomtsev‑Petviashvili (KP) hierarchy by introducing two independent integro‑differential operators, thereby creating a bidirectional hierarchy denoted as (1+1)‑BDk‑cKP. After a concise review of the standard KP hierarchy, its Lax representation L_{t_n}=