Continued fractions and integrable systems
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摘要
Stieltjes’ solution of the classical moment problem is the forerunner of inverse spectral theory. In the modern theory of completely integrable systems, the method of inverse scattering is used to obtain explicit solutions of a class of Hamiltonian systems which arise as isospectral deformations of a linear operator. In this lecture we explain how Stieltjes's formulas are used to obtain explicit solutions to a number of completely integrable systems, including discrete reductions of some nonlinear partial differential equations, and the isospectral deformations of Jacobi matrices a.k.a. Toda flows.
论文关键词:Continued fractions,Integrable systems
论文评审过程:Received 16 January 2002, Revised 14 May 2002, Available online 14 December 2002.
论文官网地址:https://doi.org/10.1016/S0377-0427(02)00607-6