Papers by Orlando Ragnisco
Nuovo Cimento C Geophysics Space Physics C, 2015
This is a paper written to celebrate the 70th birthday of our dear colleague Gaetano Vilasi where... more This is a paper written to celebrate the 70th birthday of our dear colleague Gaetano Vilasi where we collect some recent results about a couple of maximally superintegrable systems. Both the classical and the quantum version will be considered, and the corresponding solution techniques will be illustrated: namely, the spectrum generating algebra (SGA) for the classical systems and the shape invariance potentials approach (SIP) for the quantum case.
HAL (Le Centre pour la Communication Scientifique Directe), 1989
Matrix second-order differential equations and hamiltonian systems of quartic type Annales de l'I... more Matrix second-order differential equations and hamiltonian systems of quartic type Annales de l'I. H. P., section A, tome 50, n o 3 (1989), p. 369-375 <http://www.numdam.org/item?id=AIHPA_1989__50_3_369_0> © Gauthier-Villars, 1989, tous droits réservés. L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques
Теоретическая и математическая физика, 2012
arXiv (Cornell University), Apr 6, 2021
In this paper we aim at presenting a concise but also comprehensive study of time-dependent (tdep... more In this paper we aim at presenting a concise but also comprehensive study of time-dependent (tdependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations and formulate a time-dependent geometric Hamilton-Jacobi theory on lcs manifolds. In contrast to previous papers concerning locally conformal symplectic manifolds, here the introduction of the time dependency brings out interesting geometric properties, as it is the introduction of contact geometry in locally symplectic patches. To conclude, we show examples of the applications of our formalism, in particular, we present systems of differential equations with time-dependent parameters, which admit different physical interpretations as we shall point out.
Some recent results on Calogero-Gaudin systems
Dressing method and Bäcklund and Darboux transformations
CRM proceedings & lecture notes, Oct 22, 2001
Journal of Mathematical Physics, Feb 16, 2005
A special case of the Gaudin model related to the superalgebra osp(1, 2) is investigated. An exac... more A special case of the Gaudin model related to the superalgebra osp(1, 2) is investigated. An exact solution in the spin-1 2 representation is presented. A complete set of commuting observables is diagonalized, and the corresponding eigenvectors and eigenvalues are explicitly calculated. The approach used in this paper is based on the co-algebra symmetry of the model, already known from the spin-1 2 Calogero Gaudin system.
Non-isospectral deformations and Darboux transformations for the third-order spectral problem
Inverse Problems, Aug 1, 1988
ABSTRACT The authors present the class of nonlinear partial differential equations obtainable as ... more ABSTRACT The authors present the class of nonlinear partial differential equations obtainable as non-isospectral deformations of the third-order spectral problem when the spectral parameter depends on both x and t. Among these equations they have the cylindrical Boussinesq equation. Through the construction of four different Darboux transformations they construct the simplest soliton solution for the whole class and its reductions.
Dressing methodvs. classical Darboux transformation
Il Nuovo cimento della Società italiana di fisica. B, Sep 1, 1984
ABSTRACT
Bäcklund transformations for chiral field equations
Physics Letters, Feb 1, 1982
ABSTRACT
Nonlinear Evolution Equations and Dynamical Systems - Procedings of the 13th Workshop NEEDS '99 (Supplement Issue to Journal of Nonlinear Mathematical Physics): Introduction
Hyperspherical-expansion approach to nuclear bound states. IV. The limit of large A for velocity-dependent potentials
Nonlinear evolution equations solvable by the inverse spectral transform associated to the matrix Schrödinger equation of rank 4
Il Nuovo cimento della Società italiana di fisica. B, Sep 1, 1978
ABSTRACT
An example of ∂̄ problem arising in a finite difference context: Direct and inverse problem for the discrete analog of the equation ψ<sub><i>x</i><i>x</i></sub>+<i>u</i>ψ=σψ<sub><i>y</i></sub>
Journal of Mathematical Physics, Apr 1, 1987
The direct and inverse spectral problem for the discrete analog of the equation ψxx+uψ=σψy is sol... more The direct and inverse spectral problem for the discrete analog of the equation ψxx+uψ=σψy is solved in the framework of ‘‘∂̄’’ theory. The time evolution of the spectral data for the simplest nonlinear differential-difference equations associated to this linear problem is derived.
Integrable Discrete Systems
Elsevier eBooks, 2006
Recursion operator and bi‐Hamiltonian structure for integrable multidimensional lattices
Journal of Mathematical Physics, Jul 1, 1988
The recursion operator and the bi-Hamiltonian structure for an integrable two-dimensional version... more The recursion operator and the bi-Hamiltonian structure for an integrable two-dimensional version of the Toda chain are algorithmically derived from the corresponding linear problem. The intimate relation between two-dimensional theories and non-Abelian one-dimensional theories is emphasized. The analogies and differences between discrete and continuous integrable two-dimensional systems are pointed out and discussed.
Non-linear differential-difference equations with N-dependent coefficients. I
Journal of physics, Jul 1, 1979
ABSTRACT The Lax technique can be successfully employed to derive the class of nonlinear differen... more ABSTRACT The Lax technique can be successfully employed to derive the class of nonlinear differential-difference equations associated with the discrete analogue of the matrix Schrodinger spectral problem, and solvable by the spectral transform.
Nonlinear evolution equations associated with the chiral-field spectral problem
Il Nuovo cimento della Società italiana di fisica. B, Aug 1, 1985
SummaryIn this paper we derive and investigate the class of non-linear evolution equations (NEEs)... more SummaryIn this paper we derive and investigate the class of non-linear evolution equations (NEEs) associated with the linear problemϕx=λAψ. It turns out that many physically interesting NEEs pertain to this class: for instance, the chiral-field equation, the nonlinear Klein-Gordon equations, the Heisenberg and Papanicolau spin chain models, the modified Boussinesq equation, the Wadati-Konno-Ichikawa equations, etc. We display also the Bäcklund transformations for such a class and exploit them to derive in a special case the one-soliton solution.RiassuntoIn questo lavoro si deriva e studia la classe di equazioni nonlineari di evoluzione associate con il problema lineareϕx=λAψ. A questa classe appartengono molte equazione interessanti: per esempio l’equazione del campo chirale, le equazioni di Klein-Gordon non lineari, i modelli di spin di Heisenberg e Papanicolau, l’equazione di Boussinesq modificata, le equazioni di Wadati-Konno-Ichikawa, ecc. Per questa classe di equazioni sono anche mostrate le trasformate di Bäcklund, utilizzate per derivare, in un caso particolare, la soluzione ad un solitone.
Non-linear differential-difference equations with N-dependent coefficients. II
Journal of physics, Jul 1, 1979
ABSTRACT The Lax technique can be successfully employed to derive the class of nonlinear differen... more ABSTRACT The Lax technique can be successfully employed to derive the class of nonlinear differential-difference equations associated with the discrete analogue of the matrix Schrodinger spectral problem, and solvable by the spectral transform.
A unified algebraic approach to integral and discrete evolution equations
Inverse Problems, Jun 1, 1990
The authors investigate the integrability properties of discrete systems and singular integral ev... more The authors investigate the integrability properties of discrete systems and singular integral evolution equations, showing that they correspond to different reductions and different concrete realisations of the same abstract algebraic structures. In particular, they derive the bi-Hamiltonian formulation of prototype examples like the discrete sine-Gordon equation and the sine-Hilbert equation.
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Papers by Orlando Ragnisco