A new extended matrix KP hierarchy and its solutions

Abstract

Starting from the matrix KP hierarchy and adding a new τB flow, we obtain a new extended matrix KP hierarchy and its Lax representation with the symmetry constraint on squared eigenfunctions taken into account. The new hierarchy contains two sets of times tA and τB and also eigenfunctions and adjoint eigenfunctions as components. We propose a generalized dressing method for solving the extended matrix KP hierarchy and present some solutions. We study the soliton solutions of two types of (2+1)-dimensional AKNS equations with self-consistent sources and two types of Davey-Stewartson equations with selfconsistent sources.