Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials

• Published in: Journal of mathematical analysis and applications Vol. 361; no. 2; pp. 358 - 370
• Main Authors: Barrios Rolanía, D., Branquinho, A., Foulquié Moreno, A.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 2010; Elsevier
• Subjects: Differential equations; Exact sciences and technology; Fourier analysis; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Operator theory; Orthogonal polynomials; Recurrence relations; Sciences and techniques of general use; Special functions; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Recurrence relations; Orthogonal polynomials; Differential equations; Differential equation; Recurrence relation; Integrable system; Representation; Discrete system; Dynamical system; Orthogonal polynomial; Functional; Resolvent; Mathematical analysis; Application
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2009.07.025

High-order non-symmetric difference operators with complex coefficients are considered. The correspondence between dynamics of the coefficients of the operator defined by a Lax pair and its resolvent function is established. The method of investigation is based on the analysis of the moments for the operator. The solution of a discrete dynamical system is studied. We give explicit expressions for the resolvent function and, under some conditions, the representation of the vector of functionals, associated with the solution for the integrable systems.