New Classes of Toda Soliton Solutions

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 tri–diagonal 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 $\MR\bs[-1,1]$.