# Sistemas integrables discretos, polinomios matriciales ortogonales y problemas de Riemann-Hilbert Discrete integrable systems, matrix orthogonal polynomials and Riemann-Hilbert problems

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Cassatella Contra, Giovanni (2016) Sistemas integrables discretos, polinomios matriciales ortogonales y problemas de Riemann-Hilbert. [Thesis]

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## Resumen (otros idiomas)

The purpose of this Thesis is to relate the notion of integrability for discrete systems with the theory of matrix orthogonal polynomials, by using a Riemann-Hilbert approach. The study of integrable models has originated in Classical Mechanics, in relation with the problem of solving Newton's equations of motion [2]. The work of Liouville, Hamilton, Jacobi and others rmly established integrable systems as prototype modes \solvable by quadratures", i.e. by a direct integration procedure [7]. An impressive amount of research has been devoted to the study of the geometry of classical integrable and superintegrable systems [66], [82], especially in relation with the problem of separation of variables for the associated Hamilton-Jacobi equation [75]. In the second half of twentieth century, the discovery of the Inverse Scattering Method for the Korteweg-de Vries equation [42, 43] signed the beginning of a new eld of research: the study of integrable systems with in nitely many degrees of freedom, expressed in terms of nonlinear eld equations. New classes of integrable models, often encompassed in hierarchies of nonlinear partial di erential equations, were introduced. In particular, equations possessing soliton solutions found interesting applications, for instance, in classical hydrodynamics and quantum optics...

Item Type:Thesis

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica II, leída el 02/02/2016. Tesis formato europeo (compendio de artículos)

Directors:
DirectorsDirector email
Mañas Baena, Manuel
Tempesta, Piergiulio
Uncontrolled Keywords:Ecuaciones diferenciales, Riemann-Hilbert, Sistemas integrables discretos, polinomios matriciales ortogonales
Palabras clave (otros idiomas):Differential equations, Riemann-Hilbert, Discrete integrable systems, matrix orthogonal polynomials
Subjects:Sciences > Physics > Mathematical physics
ID Code:38423
Deposited On:05 Jul 2016 11:15