On the telegraph equation and the Toda equation

The variational iteration method for solving Nagumo telegraph equation

Active signal restoration for the telegraph equation

We compensate by a prefilter the distortion of an input signal along an electric line modeled by the telegraph equation. The prefilter is based on the so-called flatnessproperty of the telegraph equation. We derive the explicit equation of the filter and illustrate the relevance of our approach by a few simulations.

An Inverse Problem for the Telegraph Equation

This paper deals with the problem of state estimation for a hyperbolic equation in the presence of unknown, but bounded disturbances, on the basis of information from sensors with finite-dimensional outputs. The object of investigation is the hyperbolic telegraph equation with energy dissipation. Observability properties similar to those introduced earlier for parabolic systems ([8]) are checke...

Replica limit of the toda lattice equation.

In a recent breakthrough Kanzieper showed that it is possible to obtain exact nonperturbative random matrix results from the replica limit of the corresponding Painlevé equation. In this article we analyze the replica limit of the Toda lattice equation and obtain exact expressions for the two-point function of the Gaussian unitary ensemble and the resolvent of the chiral unitary ensemble. In th...

Direct “delay” Reductions of the Toda Equation

A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differentialdifference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classic...