FERAPONTOV, E. and MOSS, J., 2014. Characteristic integrals in 3D and linear degeneracy. Journal of Nonlinear Mathematical Physics, DOI: 10.1080/14029251.2014.900993.
Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable equations. In this paper we discuss characteristic integrals in 3D and demonstrate that, for a class of second order linearly degenerate dispersionless integrable PDEs, the corresponding characteristic integrals are parametrised by points on the Veronese variety.
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Nonlinear Mathematical Physics on 13/05/2016, available online: http://dx.doi.org/10.1080/14029251.2014.900993.