scispace - formally typeset
Search or ask a question
Author

Matteo Petrera

Bio: Matteo Petrera is an academic researcher from Technical University of Berlin. The author has contributed to research in topics: Integrable system & Discretization. The author has an hindex of 17, co-authored 80 publications receiving 961 citations. Previous affiliations of Matteo Petrera include Roma Tre University & Istituto Nazionale di Fisica Nucleare.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields is given.
Abstract: We give an overview of the integrability of the Hirota-Kimura discretizationmethod applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.

67 citations

Journal ArticleDOI
TL;DR: In this article, the authors give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields.
Abstract: We give an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.

60 citations

Journal ArticleDOI
TL;DR: In this article, the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list were mapped into the dis- crete Schrodinger spectral problem associated with Volterra-type equations.
Abstract: We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler-Bobenko-Suris (ABS) list into the dis- crete Schrodinger spectral problem associated with Volterra-type equations. We show that the ABS equations correspond to Backlund transformations for some particular cases of the discrete Krichever-Novikov equation found by Yamilov (YdKN equation). This enables us to construct new generalized symmetries for the ABS equations. The same can be said about the generalizations of the ABS equations introduced by Tongas, Tsoubelis and Xenitidis. All of them generate Backlund transformations for the YdKN equation. The higher order generalized symmetries we construct in the present paper confirm their integrability.

53 citations

Journal ArticleDOI
TL;DR: In this article, a remarkable integrable discretization of the so (3) Euler top introduced by Hirota and Kimura is presented, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions.
Abstract: This paper deals with a remarkable integrable discretization of the so (3) Euler top introduced by Hirota and Kimura. Such a discretization leads to an explicit map, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions. Our goal is the construction of its Hamiltonian formulation. After giving a simplified and streamlined presentation of their results, we provide a bi-Hamiltonian structure for this discretization, thus proving its integrability in the standard Liouville-Arnold sense (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

53 citations

Journal ArticleDOI
TL;DR: Hirota and Kimura as mentioned in this paper presented integrable discretizations of the Euler and the Lagrange top, given by birational maps, which is a specialization to the integrability of a general context.
Abstract: R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general d...

47 citations


Cited by
More filters
Journal ArticleDOI
TL;DR: This paper discusses Walker Structures, Lorentzian Walker Manifolds, and the Spectral Geometry of the Curvature Tensor.
Abstract: * Basic Algebraic Notions* Basic Geometrical Notions* Walker Structures* Three-Dimensional Lorentzian Walker Manifolds* Four-Dimensional Walker Manifolds* The Spectral Geometry of the Curvature Tensor* Hermitian Geometry* Special Walker Manifolds

112 citations

01 Jan 2016
TL;DR: The function theory in polydiscs is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
Abstract: Thank you very much for reading function theory in polydiscs. Maybe you have knowledge that, people have look numerous times for their chosen novels like this function theory in polydiscs, but end up in harmful downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they cope with some malicious bugs inside their laptop. function theory in polydiscs is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the function theory in polydiscs is universally compatible with any devices to read.

78 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that Kahan's discretization of quadratic vector fields is equivalent to a Runge-Kutta method, which produces large classes of integrable rational mappings in two and three dimensions.
Abstract: We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge–Kutta method. When the vector field is Hamiltonian on either a symplectic vector space or a Poisson vector space with constant Poisson structure, the map determined by this discretization has a conserved modified Hamiltonian and an invariant measure, a combination previously unknown amongst Runge–Kutta methods applied to nonlinear vector fields. This produces large classes of integrable rational mappings in two and three dimensions, explaining some of the integrable cases that were previously known.

71 citations

Journal ArticleDOI
TL;DR: In this article, the generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list, and a few integrability conditions suitable for testing and classifying the equations of this class are derived.
Abstract: The generalized symmetry method is applied to a class of completely discrete equations including the Adler–Bobenko–Suris list. Assuming the existence of a generalized symmetry, we derive a few integrability conditions suitable for testing and classifying the equations of this class. Those conditions are used at the end to test for integrability discretizations of some well-known hyperbolic equations.

71 citations

Journal ArticleDOI
TL;DR: In this paper, an overview of the integrability of the Hirota-Kimura discretization method applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields is given.
Abstract: We give an overview of the integrability of the Hirota-Kimura discretizationmethod applied to algebraically completely integrable (a.c.i.) systems with quadratic vector fields. Along with the description of the basic mechanism of integrability (Hirota-Kimura bases), we provide the reader with a fairly complete list of the currently available results for concrete a.c.i. systems.

67 citations