On Toda lattices and orthogonal polynomials

[摘要] First, we derive a simple connection between Toda and Langmuir lattices and give a characterization of Toda lattices with the help of Stieltjes functions, Then it is shown how to generate by orthogonal polynomials in an elementary way periodic and almost periodic Toda lattices. The particles of the Toda lattice are not even restricted, as usual, to move on the real line, they may also move in the complex plane. With the help of this result, for special cases explicit solutions are obtained in terms of elliptic functions. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-08-01

[效力级别]  Proceedings Paper

[关键词] polynomials orthogonal on several intervals;Pade-approximants of square-root functions;periodic recurrence coefficients;periodic lattices;elliptic functions