Geodesic
A new extended matrix KP hierarchy and its solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 222-238 Cet article a éte moissonné depuis la source Math-Net.Ru

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Starting from the matrix KP hierarchy and adding a new $\tau_{B}$ 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 $t_{A}$ and $\tau_{B}$ 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 self-consistent sources.
Keywords: extended matrix KP hierarchy, Lax representation, generalized dressing method, $2+1$ AKNS equation with self-consistent sources, Davey–Stewartson equation with self-consistent sources. 
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Yehui Huang; Xiaojun Liu; Yuqin Yao; Yunbo Zeng. A new extended matrix KP hierarchy and its solutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 222-238. http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a5/

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