arXiv subjects

Matteo Petrera

Publications and source records attributed to Matteo Petrera.

41 records · Page 3Linked to original sources

arXiv2005

Discrete Reductive Perturbation Technique

We expand a partial difference equation (P$Δ$E) on multiple lattices and obtain the P$Δ$E which governs its far field behaviour. The perturbative--reductive approach is here performed on well known nonlinear P$Δ$Es, both integrable and non integrable. We study the cases of the lattice modified Korteweg--de Vries (mKdV) equation, the Hietarinta equation, the lattice Volterra--Kac--Van Moerbeke (VKVM) equation and a non integrable lattice KdV equation. Such reductions allow us to obtain many new P$Δ$Es of the nonlinear Schrödinger (NLS) type.

math-ph↗

arXiv2005

Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))$ symmetry

We consider a Gaudin model related to the q-deformed superalgebra ${\CU}_q(\mathfrak{osp}(1 | 2))$. We present an exact solution to that system diagonalizing a complete set of commuting observables, and providing the corresponding eigenvectors and eigenvalues. The approach used in this paper is based on the coalgebra supersymmetry of the model.

math-ph↗

arXiv2004

Algebraic extensions of Gaudin models

We perform a Inönü--Wigner contraction on Gaudin models, showing how the integrability property is preserved by this algebraic procedure. Starting from Gaudin models we obtain new integrable chains, that we call Lagrange chains, associated to the same linear $r$-matrix structure. We give a general construction involving rational, trigonometric and elliptic solutions of the classical Yang-Baxter equation. Two particular examples are explicitly considered: the rational Lagrange chain and the trigonometric one. In both cases local variables of the models are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting tops.

nlin.SI↗

arXiv2004

Bäcklund transformations for the rational Lagrange chain

We consider a long--range homogeneous chain where the local variables are the generators of the direct sum of $N$ $\mathfrak{e}(3)$ interacting Lagrange tops. We call this classical integrable model rational ``Lagrange chain'' showing how one can obtain it starting from $\mathfrak{su}(2)$ rational Gaudin models. Moreover we construct one- and two--point integrable maps (Bäcklund transformations).

nlin.SI↗

arXiv2004

Separation of variables and Bäcklund transformations for the symmetric Lagrange top

We construct the 1- and 2-point integrable maps (Bäcklund transformations) for the symmetric Lagrange top. We show that the Lagrange top has the same algebraic Poisson structure that belongs to the $sl(2)$ Gaudin magnet. The 2-point map leads to a real time-discretization of the continuous flow. Therefore, it provides an integrable numerical scheme for integrating the physical flow. We illustrate the construction by few pictures of the discrete flow calculated in MATLAB.

nlin.SI↗