Solving bi-directional soliton equations in the KP hierarchy by gauge transformation

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dc.creatorHe, Jingsong
dc.creatorCheng, Yi
dc.creatorRoemer, Rudolf A.
dc.date2005-03-11
dc.date2006-02-21
dc.date.accessioned2026-07-07T06:38:35Z
dc.date.available2026-07-07T06:38:35Z
dc.descriptionWe present a systematic way to construct solutions of the (n=5)-reduction of the BKP and CKP hierarchies from the general tau function 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 exp(i epsilon). Furthermore, we show that the soliton solutions of the n-reduction of the BKP and CKP hierarchies with n= 2 j +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 exp(i epsilon). Based on this classification, we detail the existence of two-peak solitons of the n-reduction from the Grammian tau 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.
dc.description32 pages, 8 figures, high quality figures can be downloaded from http://eprints.csc.warwick.ac.uk/archive/00000103/
dc.identifierhttps://arxiv.org/abs/math-ph/0503028
dc.identifierhttp://arxiv.org/abs/math-ph/0503028
dc.identifierJHEP 0603 (2006) 103
dc.identifierdoi:10.1088/1126-6708/2006/03/103
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100790
dc.subjectMathematical Physics
dc.subject35Q51; 37K10; 82C23
dc.titleSolving bi-directional soliton equations in the KP hierarchy by gauge transformation
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