Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
| dc.creator | Tsuchida, Takayuki | |
| dc.creator | Wolf, Thomas | |
| dc.date | 2004-12-01 | |
| dc.date | 2005-07-14 | |
| dc.date.accessioned | 2026-07-07T06:24:30Z | |
| dc.date.available | 2026-07-07T06:24:30Z | |
| dc.description | We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of 2nd order systems with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made. | |
| dc.description | 60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus several minor changes, to appear in J.Phys.A | |
| dc.identifier | https://arxiv.org/abs/nlin/0412003 | |
| dc.identifier | http://arxiv.org/abs/nlin/0412003 | |
| dc.identifier | J. Phys. A: Math. Gen. 38 (2005) 7691-7733 | |
| dc.identifier | doi:10.1088/0305-4470/38/35/006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96565 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | Mathematical Physics | |
| dc.title | Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I | |
| dc.type | text |