On the telegraph equation and the Toda equation (Q1057426)

The Toda equation referred in this paper reads XY log \(t_ n=t_{n+1}t_{n-1}/t^ 2_ n\), where \(X=\partial /\partial x\), \(Y=\partial /\partial y\) and \(t_ n=t_ n(x,y)\). The author gives a Bäcklund transformation of the Toda equation in terms of solutions of the telegraph equation \((XY+1)u_ n=0\). Using various solutions \(u_ n\) the author obtains rational solutions, Bessel function solutions and solutions expressed by hypergeometric functions.