
The Library
Solving bi-directional soliton equations in the KP hierarchy by gauge transformation
Tools
He, Jingsong, Cheng, Yi and Roemer, Rudolf A. (2006) Solving bi-directional soliton equations in the KP hierarchy by gauge transformation. Journal of High Energy Physics (Online), Vol.3 . doi:10.1088/1126-6708/2006/03/103 ISSN 1029-8479.
![]()
|
PDF
WRAP_Roemer_Solving-bi-drectional.pdf - Requires a PDF viewer. Download (741Kb) |
Official URL: http://dx.doi.org/10.1088/1126-6708/2006/03/103
Abstract
We present a systematic way to construct solutions of the (n = 5)-reduction of the BKP and CKP hierarchies from the general τ function τn+k of the KP hierarchy. We obtain the one-soliton, two-soliton, and periodic solution for the bi-directional Sawada-Kotera (bSK), the bi-directional Kaup-Kupershmidt (bKK) and also the bi-directional Satsuma-Hirota (bSH) equation. Different solutions such as left- and right-going solitons are classified according to the symmetries of the 5th roots of eiε. Furthermore, we show that the soliton solutions of the n-reduction of the BKP and CKP hierarchies with n = 2j+1, j = 1,2,3,..., can propagate along j directions in the 1+1 space-time domain. Each such direction corresponds to one symmetric distribution of the nth roots of eiε. Based on this classification, we detail the existence of two-peak solitons of the n-reduction from the Grammian τ function of the sub-hierarchies BKP and CKP. If n is even, we again find two-peak solitons. Last, we obtain the ``stationary" soliton for the higher-order KP hierarchy.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Centre for Scientific Computing Faculty of Science, Engineering and Medicine > Science > Physics |
||||
Library of Congress Subject Headings (LCSH): | Solitons, Kadomtsev-Petviashvili hierarchy | ||||
Journal or Publication Title: | Journal of High Energy Physics (Online) | ||||
Publisher: | Institute of Physics Publishing | ||||
ISSN: | 1029-8479 | ||||
Official Date: | 31 March 2006 | ||||
Dates: |
|
||||
Volume: | Vol.3 | ||||
DOI: | 10.1088/1126-6708/2006/03/103 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Funder: | China, Guo jia zi ran ke xue ji jin wei yuan hui (China) [National Natural Science Foundation of China] (NSFC), University of Warwick | ||||
Grant number: | 10301030 (NSFC) |
Request changes or add full text files to a record
Repository staff actions (login required)
![]() |
View Item |