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 [10.1088/0951-7715/29/9/2715].

Deformations of non-semisimple Poisson pencils of hydrodynamic type

DELLA VEDOVA, ALBERTO
Primo
;
LORENZONI, PAOLO
Secondo
;
2016

Abstract

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.
Articolo in rivista - Articolo scientifico
Balinskǐ-Novikov algebras; bi-Hamiltonian structures; complete lift;
Balinskǐ-Novikov algebras; bi-Hamiltonian structures; complete lift; Statistical and Nonlinear Physics; Mathematical Physics; Physics and Astronomy (all); Applied Mathematics
English
2016
29
9
2715
2754
reserved
DELLA VEDOVA, A., Lorenzoni, P., Savoldi, A. (2016). Deformations of non-semisimple Poisson pencils of hydrodynamic type. NONLINEARITY, 29(9), 2715-2754 [10.1088/0951-7715/29/9/2715].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/143803
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