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Solving bi-directional soliton equations in the KP hierarchy by gauge transformation
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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
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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 | ||||
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| Subjects: | Q Science > QC Physics | ||||
| Divisions: | Faculty of Science > Centre for Scientific Computing Faculty of Science > Physics |
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| 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: |
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| Volume: | Vol.3 | ||||
| DOI: | 10.1088/1126-6708/2006/03/103 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access | ||||
| 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) |
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