Two-Dimensional Toda Lattice Equations

Innnite Dimensional Lie Groups and the Two-dimensional Toda Lattice

1 Darboux Transformations for Nonlocal Two – Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two–dimensional periodic A n−1 Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The solutio...

Toda Lattice Hierarchy and Generalized String Equations

String equations of the p-th generalized Kontsevich model and the compactified c = 1 string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model at p = −1 does not coincide with the c = 1 string theory at self-dual radius. A broader family of solutions of the Toda lattice hierarchy includi...

University of Cambridge Conservative Methods for the Toda Lattice Equations Conservative Methods for the Toda Lattice Equations

We are concerned with the numerical integration of the Toda lattice equations by using diierent conservative methods. Numerical experiments suggest that the global error for isospectral schemes decreases exponentially with time but it is almost constant for either symplectic or more general integrators. We provide a theoretical explanation for these experimental ndings.

A Rational Flow for the Periodic Toda Lattice Equations

Dedicated to my long-time friend and colleague, Paul Fuhrmann, on the occasion of his 60 th birthday Abstract We show how a certain class of Hamiltonian systems give rise to diierential equations on spaces of matrices whose elements are rational functions. In particular, we reinterpret the results of Kac and van Moerbeke on the periodic Toda lattice in terms of such diierential equations and re...