Department of Mathematics, Brock University,
500 Glenridge Avenue, St.Catharines,
Ontario, L2S 3A1 CANADA
Classification of polynomial integrable systems with one scalar and one vector unknown
We perform a symmetry classification of polynomial integrable systems with one scalar and one vector unknown. We assume the homogeneity of systems under a suitable weighting of variables and consider several distinct weightings. In each case, we give the complete lists of second and third order systems with a higher symmetry. For all but a few systems in the lists, we show that the system (or, at least its subsystem) admits either a Lax representation or a linearizing transformation.
The highlight is the classification in the case of Burgers/pKdV/mKdV weighting. The results generalize recent work of Foursov and Olver.