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TMF, 2016, Volume 186, Number 3, Pages 357–370 (Mi tmf8959)  

This article is cited in 2 scientific papers (total in 2 papers)

Bilinear identities for an extended B-type Kadomtsev–Petviashvili hierarchy

Runliang Lina, Tiancheng Caoa, Xiaojun Liub, Yunbo Zenga

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

Abstract: We construct bilinear identities for wave functions of an extended B-type Kadomtsev–Petviashvili (BKP) hierarchy containing two types of $(2{+}1)$-dimensional Sawada–Kotera equations with a self-consistent source. Introducing an auxiliary variable corresponding to the extended flow for the BKP hierarchy, we find the $\tau$-function and bilinear identities for this extended BKP hierarchy. The bilinear identities generate all the Hirota bilinear equations for the zero-curvature forms of this extended BKP hierarchy. As examples, we obtain the Hirota bilinear equations for the two types of $(2{+}1)$-dimensional Sawada–Kotera equations in explicit form.

Keywords: BKP hierarchy, self-consistent source, bilinear identity, tau function, Hirota bilinear form

Funding Agency Grant Number
National Natural Science Foundation of China 11471182
11171175
11201477
This research is supported by the National Natural Science Foundation of China (Grant Nos. 11471182, 11171175, and 11201477)

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf8959

Full text: PDF file (435 kB)
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English version:
Theoretical and Mathematical Physics, 2016, 186:3, 307–319

Bibliographic databases:

PACS: 02.30.Ik
MSC: 35Q51, 37K10
Received: 02.05.2015

Citation: Runliang Lin, Tiancheng Cao, Xiaojun Liu, Yunbo Zeng, “Bilinear identities for an extended B-type Kadomtsev–Petviashvili hierarchy”, TMF, 186:3 (2016), 357–370; Theoret. and Math. Phys., 186:3 (2016), 307–319

Citation in format AMSBIB
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\by Runliang~Lin, Tiancheng~Cao, Xiaojun~Liu, Yunbo~Zeng
\paper Bilinear identities for an~extended B-type Kadomtsev--Petviashvili hierarchy
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\vol 186
\issue 3
\pages 357--370
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\transl
\jour Theoret. and Math. Phys.
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\vol 186
\issue 3
\pages 307--319
\crossref{https://doi.org/10.1134/S0040577916030016}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Runliang Lin, Yukun Du, “Generalized Darboux transformation for the discrete Kadomtsev–Petviashvili equation with self-consistent sources”, Theoret. and Math. Phys., 196:3 (2018), 1320–1332  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Geng L., Chen H., Li N., Cheng J., “Bilinear Identities and Squared Eigenfunction Symmetries of the Bcr-Kp Hierarchy”, J. Nonlinear Math. Phys., 26:3 (2019), 404–419  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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