Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I

dc.creatorTsuchida, Takayuki
dc.creatorWolf, Thomas
dc.date2004-12-01
dc.date2005-07-14
dc.date.accessioned2026-07-07T06:24:30Z
dc.date.available2026-07-07T06:24:30Z
dc.descriptionWe 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.description60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus several minor changes, to appear in J.Phys.A
dc.identifierhttps://arxiv.org/abs/nlin/0412003
dc.identifierhttp://arxiv.org/abs/nlin/0412003
dc.identifierJ. Phys. A: Math. Gen. 38 (2005) 7691-7733
dc.identifierdoi:10.1088/0305-4470/38/35/006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96565
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.titleClassification of polynomial integrable systems of mixed scalar and vector evolution equations. I
dc.typetext

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