Hone, Andrew N.W., Wang, Jing Ping (2008) Integrable peakon equations with cubic nonlinearity. Journal of Physics A: Mathematical and Theoretical, 41 . ISSN 1751-8113. (doi:37200210.1088/1751-8113/41/37/372002) (KAR id:15691)
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Official URL: http://dx.doi.org/10.1088/1751-8113/41/37/372002 |
Abstract
We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao.
Item Type: | Article |
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DOI/Identification number: | 37200210.1088/1751-8113/41/37/372002 |
Additional information: | Article identifier = 372002 |
Uncontrolled keywords: | Exactly Solvable and Integrable Systems (nlin.SI); Pattern Formation and Solitons (nlin.PS) |
Subjects: | Q Science |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Andrew Hone |
Date Deposited: | 20 Apr 2009 14:30 UTC |
Last Modified: | 16 Nov 2021 09:53 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/15691 (The current URI for this page, for reference purposes) |
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