Journal of Nonlinear Mathematical Physics

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Volume 25, Issue 2, March 2018, Pages 309 - 323

Bilinear Identities and Hirota’s Bilinear Forms for the (γn, σk)-KP Hierarchy

Authors
Yuqin Yao
Departmentof Applied Mathematics, China Agricultural University, Beijing, 100083, People’s Republic of China,yyqinw@126.com
Juhui Zhang
Departmentof Applied Mathematics, China Agricultural University, Beijing, 100083, People’s Republic of China
Runliang Lin
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China
Xiaojun Liu
Departmentof Applied Mathematics, China Agricultural University, Beijing, 100083, People’s Republic of China
Yehui Huang
School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, People’s Republic of China
Received 31 August 2017, Accepted 8 January 2018, Available Online 6 January 2021.
DOI
10.1080/14029251.2018.1452675How to use a DOI?
Keywords
(γn, σk)-KP hierarchy; bilinear identity; τ-function; Hirota's bilinear form
Abstract

In this paper, we discuss how to construct the bilinear identities for the wave functions of the (γn, σk)-KP hierarchy and its Hirota’s bilinear forms. First, based on the corresponding squared eigenfunction symmetry of the KP hierarchy, we prove that the wave functions of the (γn, σk)-KP hierarchy are equal to the bilinear identities given in Sec.3 by introducing N auxiliary parameters zi, i = 1, 2, …, N. Next, we derived the bilinear equations for the tau-function of the (γn, σk)-KP hierarchy. Then, we obtain the bilinear equations for the taufunction of the mixed type of KP equation with self-consistent sources (KPESCS), which includes both the first and the second type of KPESCS as special cases by setting n = 2 and k = 3. Finally, using the relation between the Hirota bilinear derivatives and the usual partial derivatives, we show the procedure of translating the Hirota’s bilinear equations into the mixed type of KPESCS.

Copyright
© 2018 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 2
Pages
309 - 323
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2018.1452675How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Yuqin Yao
AU  - Juhui Zhang
AU  - Runliang Lin
AU  - Xiaojun Liu
AU  - Yehui Huang
PY  - 2021
DA  - 2021/01/06
TI  - Bilinear Identities and Hirota’s Bilinear Forms for the (γn, σk)-KP Hierarchy
JO  - Journal of Nonlinear Mathematical Physics
SP  - 309
EP  - 323
VL  - 25
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1452675
DO  - 10.1080/14029251.2018.1452675
ID  - Yao2021
ER  -