Integrable peakon equations with cubic nonlinearity
| dc.creator | Hone, Andrew N. W. | |
| dc.creator | Wang, Jing Ping | |
| dc.date | 2008-05-28 | |
| dc.date.accessioned | 2026-07-07T09:41:19Z | |
| dc.date.available | 2026-07-07T09:41:19Z | |
| dc.description | 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. | |
| dc.description | Submitted to Journal of Physics A: Mathematical and Theoretical | |
| dc.identifier | https://arxiv.org/abs/0805.4310 | |
| dc.identifier | http://arxiv.org/abs/0805.4310 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161788 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Pattern Formation and Solitons | |
| dc.title | Integrable peakon equations with cubic nonlinearity | |
| dc.type | text |