On the (modified) Kadomtsev-Petviashvili hierarchy (Q1343181)

The authors suggest a new approach to the Kadomtsev-Petviashvili (KP) hierarchy and the corresponding mKP hierarchy. The main idea is to replace the usual first-order formal pseudo-differential Lax operator \(L_1 = \partial_x + \sum^{-1}_{j = - \infty} u_j \partial^j_x \) by an \(n\)-th order formal pseudo-differential operator \(L_n = \partial^n_x + \sum^{n - 2}_{j = - \infty} q_j \partial^j_x\), \(n \geq 2\). Investigating the factorizations of \(L_n\) into \(n - 1\) first-order formal differential operators, new KP Bäcklund transformations are obtained. The efficiency of the approach proposed is illustrated by examples.