F. Gesztesy and W. Renger
New Classes of Toda Soliton Solutions
(65K, amslatex)
ABSTRACT. We provide a detailed investigation of limits of N-soliton solutions of
the Toda lattice as N tends to infinity. Our principal results yield new
classes of Toda solutions including, in particular, new kinds of
soliton-like (i.e., reflectionless) solutions. As a byproduct we solve an
inverse spectral problem for one-dimensional Jacobi operators and
explicitly construct tridiagonal matrices that yield a purely absolutely
continuous spectrum in (-1,1) and give rise to an eigenvalue spectrum
that includes any prescribed countable and bounded subset of R\[-1,1].