Determinant Formulas for the Toda and Discrete Toda Equations

Abstract

Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the $\tau$ functions for the Painlevé equations is also discussed.

16pages, LaTeX using theorem.sty

References in corpus (1)

• Rational Solutions for the Discrete Painlevé II Equation

Cited by in corpus (9)

• Application of the $\tau$-Function Theory of Painlevé Equations to Random Matrices: PIV, PII and the GUE
• Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons
• Special polynomials related to the supersymmetric eight-vertex model: A summary
• Generating Function Associated with the Rational Solutions of the Painlevé II Equation
• A Symmetric System of Mixed Painleve III - V Equations and its Integrable Origin
• A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions
• Non-Abelian discrete Toda chains and related lattices
• Elliptic pfaffians and solvable lattice models
• Symmetries in the third Painlevé equation arising from the modified Pohlmeyer-Lund-Regge hierarchy