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TMF, 2011, Volume 167, Number 2, Pages 222–238 (Mi tmf6636)  

This article is cited in 6 scientific papers (total in 6 papers)

A new extended matrix KP hierarchy and its solutions

Yehui Huanga, Xiaojun Liub, Yuqin Yaob, Yunbo Zenga

a Department of Mathematical Science, Tsinghua University, Beijing, China
b Department of Applied Mathematics, China Agricultural University, Beijing, China

Abstract: 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

DOI: https://doi.org/10.4213/tmf6636

Full text: PDF file (430 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 167:2, 590–605

Bibliographic databases:

Received: 05.09.2010
Revised: 26.09.2010

Citation: Yehui Huang, Xiaojun Liu, Yuqin Yao, Yunbo Zeng, “A new extended matrix KP hierarchy and its solutions”, TMF, 167:2 (2011), 222–238; Theoret. and Math. Phys., 167:2 (2011), 590–605

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Huang Ye-Hui, Yao Yu-Qin, Zeng Yun-Bo, “A new $(\gamma_A,\sigma_B)$-matrix KP hierarchy and its solutions”, Commun. Theor. Phys., 57:4 (2012), 515–522  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Lin R., Liu X., Zeng Yu., “Bilinear Identities and Hirota's Bilinear Forms for an Extended Kadomtsev-Petviashvili Hierarchy”, J. Nonlinear Math. Phys., 20:2 (2013), 214–228  crossref  mathscinet  isi  scopus
    3. Chvartatskyi O.I. Sydorenko Yu.M., “A New Bidirectional Generalization of (2+1)-Dimensional Matrix K-Constrained Kadomtsev-Petviashvili Hierarchy”, J. Math. Phys., 54:11 (2013), 113508  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Doliwa A., Lin R., “Discrete KP Equation With Self-Consistent Sources”, Phys. Lett. A, 378:28-29 (2014), 1925–1931  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Oleksandr Chvartatskyi, Yuriy Sydorenko, “Darboux Transformations for $(2+1)$-Dimensional Extensions of the KP Hierarchy”, SIGMA, 11 (2015), 028, 20 pp.  mathnet  crossref  mathscinet
    6. Chvartatskyi O., Dimakis A., Mueller-Hoissen F., “Self-Consistent Sources for Integrable Equations Via Deformations of Binary Darboux Transformations”, Lett. Math. Phys., 106:8 (2016), 1139–1179  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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