We study the deformations of two-component non-semisimple Poisson pencils of hydrodynamic type associated with Balinskǐ-Novikov algebras. We show that in most cases the second order deformations are parametrized by two functions of a single variable. We find 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 exceptional cases the second order deformations are parametrized by four functions. Among these two are invariants and two are related to a two-parameter family of truncated structures. We also study the lift of the deformations of n-component semisimple structures. This example suggests that deformations of non-semisimple pencils corresponding to the lifted invariant parameters are unobstructed.
Della Vedova, A., Lorenzoni, P., & Savoldi, A. (2016). Deformations of non-semisimple Poisson pencils of hydrodynamic type. NONLINEARITY, 29(9), 2715-2754.
Citazione: | Della Vedova, A., Lorenzoni, P., & Savoldi, A. (2016). Deformations of non-semisimple Poisson pencils of hydrodynamic type. NONLINEARITY, 29(9), 2715-2754. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | Si |
Titolo: | Deformations of non-semisimple Poisson pencils of hydrodynamic type |
Autori: | Della Vedova, A; Lorenzoni, P; Savoldi, A |
Autori: | DELLA VEDOVA, ALBERTO (Primo) LORENZONI, PAOLO (Secondo) |
Data di pubblicazione: | 2016 |
Lingua: | English |
Rivista: | NONLINEARITY |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/0951-7715/29/9/2715 |
Appare nelle tipologie: | 01 - Articolo su rivista |