Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm

DOI10.1088/0951-7715/24/8/006zbMath1223.37088arXiv1005.0482OpenAlexW3100812710MaRDI QIDQ3173384

Paul E. Spicer, Frank W. Nijhoff, Peter H. van der Kamp

Publication date: 10 October 2011

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.0482

zbMATH Keywords

formal orthogonal polynomialspartial difference equationLax pairsmathematical physicsdiscrete-time Toda equationhigher order analogue of the discrete-time Toda (HADT)quotient-quotient-difference (QQD) scheme

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Partial difference equations (39A14) Numerical methods for difference equations (65Q10)

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Multidimensional Toda lattices: continuous and discrete time ⋮ Orthogonal polynomials on a class of planar algebraic curves ⋮ Christoffel transformations for (partial-)skew-orthogonal polynomials and applications ⋮ Algebraic entropy of (integrable) lattice equations and their reductions ⋮ Duality for discrete integrable systems II ⋮ On three-term recurrence and Christoffel–Darboux identity for orthogonal rational functions on the real line ⋮ Nonisospectral extension of Schur flow with determinant solution and orthogonal polynomials on the unit circle

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