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arXiv · 1506.02309

Deformations of non semisimple Poisson pencils of hydrodynamic type

Alberto Della Vedova·Paolo Lorenzoni·Andrea Savoldi
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Abstract

We study deformations of two-component non semisimple Poisson pencils of hydrodynamic type associated with Balinski\vı-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.

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Alberto Della Vedova, Paolo Lorenzoni, Andrea Savoldi. 2015-06-22. Deformations of non semisimple Poisson pencils of hydrodynamic type. https://doi.org/10.1088/0951-7715%2F29%2F9%2F2715

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