QUASIDETERMINANT SOLUTIONS OF THE EXTENDED NONCOMMUTATIVE KADOMTSEV-PETVIASHVILI HIERARCHY

摘要

We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev-Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.