Deformations of non semisimple Poisson pencils of hydrodynamic type
Abstract
We study deformations of two-component non semisimple Poisson pencils of hydrodynamic type associated with Balinski\v{\i}-Novikov algebras. We show that in most cases the second order deformations are parametrized by two functions of a single variable. It turns out that one function is invariant with respect to the subgroup of Miura transformations preserving the dispersionless limit and another function is related to a one-parameter family of truncated structures. In two expectional cases the second order deformations are parametrized by four functions. Among them two are invariants and two are related to a two-parameter family of truncated structures. We also study the lift of deformations of n-component semisimple structures. This example suggests that deformations of non semisimple pencils corresponding to the lifted invariant parameters are unobstructed.
Keywords
Cite
@article{arxiv.1506.02309,
title = {Deformations of non semisimple Poisson pencils of hydrodynamic type},
author = {Alberto Della Vedova and Paolo Lorenzoni and Andrea Savoldi},
journal= {arXiv preprint arXiv:1506.02309},
year = {2016}
}
Comments
45 pages, references added