Zobrazeno 1 - 10
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pro vyhledávání: '"Vitolo, R."'
Autor:
Opanasenko, S., Vitolo, R.
Publikováno v:
Proc. R. Soc. A 480 (2024), 20240249
We study a class of nonlinear PDEs that admit the same bi-Hamiltonian structure as WDVV equations: a Ferapontov-type first-order Hamiltonian operator and a homogeneous third-order Hamiltonian operator in a canonical Doyle--Potemin form, which are com
Externí odkaz:
http://arxiv.org/abs/2407.17189
Autor:
Lorenzoni, P., Vitolo, R.
We study algebraic and projective geometric properties of Hamiltonian trios determined by a constant coefficient second-order operator and two first-order localizable operators of Ferapontov type. We show that first-order operators are determined by
Externí odkaz:
http://arxiv.org/abs/2311.13932
Publikováno v:
Nonlinearity 37 (2024), no. 2, paper no. 025001, 35 pages
We show that the equivalence classes of deformations of localizable semisimple Poisson pencils of hydrodynamic type with respect to the action of the Miura-reciprocal group contain a local representative and are in one-to-one correspondence with the
Externí odkaz:
http://arxiv.org/abs/2301.04475
Autor:
Lorenzoni, P., Vitolo, R.
Publikováno v:
Journal of Geometry and Physics Vol. 149 (2020) 103573. Part of a Special Issue, see https://gdeq.org/SIJSK70
Poisson brackets between conserved quantities are a fundamental tool in the theory of integrable systems. The subclass of weakly nonlocal Poisson brackets occurs in many significant integrable systems. Proving that a weakly nonlocal differential oper
Externí odkaz:
http://arxiv.org/abs/1909.07695
Publikováno v:
Studies in Applied Mathematics (2020)
We compare three different ways of checking the Jacobi identity for weakly nonlocal Poisson brackets using the theory of distributions, of pseudodifferential operators and of Poisson vertex algebras, respectively. We show that the three approaches le
Externí odkaz:
http://arxiv.org/abs/1903.08204
Autor:
Pavlov, M. V., Vitolo, R. F.
Publikováno v:
Journal of Physics A: Mathematical and Theoretical, Letter, Volume 52, Number 20 (2019)
The Oriented Associativity equation plays a fundamental role in the theory of Integrable Systems. In this paper we prove that the equation, besides being Hamiltonian with respect to a first-order Hamiltonian operator, has a third-order non-local homo
Externí odkaz:
http://arxiv.org/abs/1812.01413
Autor:
Vitolo, R.
Publikováno v:
Computer Physics Communications (2019)
Hamiltonian operators are used in the theory of integrable partial differential equations to prove the existence of infinite sequences of commuting symmetries or integrals. In this paper it is illustrated the new Reduce package \cde for computations
Externí odkaz:
http://arxiv.org/abs/1808.03902
Publikováno v:
Journal of Geometry and Physics Volume 138, April 2019, Pages 285-296
Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric type. Hamiltonian operators within this class are defined by a Monge me
Externí odkaz:
http://arxiv.org/abs/1805.00746
Publikováno v:
In Computer Physics Communications May 2022 274
Publikováno v:
Lett. Math. Phys. 108, Issue 6 (2018), 1525-1550
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in
Externí odkaz:
http://arxiv.org/abs/1703.06173