Geodesic
A~new extended matrix KP hierarchy and its solutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 2, pp. 222-238

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2011_167_2_a5,
     author = {Yehui Huang and Xiaojun Liu and Yuqin Yao and Yunbo Zeng},
     title = {A~new extended matrix {KP} hierarchy and its solutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {222--238},
     publisher = {mathdoc},
     volume = {167},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a5/}
}
TY  - JOUR
AU  - Yehui Huang
AU  - Xiaojun Liu
AU  - Yuqin Yao
AU  - Yunbo Zeng
TI  - A~new extended matrix KP hierarchy and its solutions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 222
EP  - 238
VL  - 167
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a5/
LA  - ru
ID  - TMF_2011_167_2_a5
ER  - 
%0 Journal Article
%A Yehui Huang
%A Xiaojun Liu
%A Yuqin Yao
%A Yunbo Zeng
%T A~new extended matrix KP hierarchy and its solutions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 222-238
%V 167
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2011_167_2_a5/
%G ru
%F TMF_2011_167_2_a5
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/