Reflectionless Analytic Difference Operators II. Relations to Soliton Systems

DOI

10.2991/jnmp.2001.8.2.8How to use a DOI?

Abstract

This is the second part of a series of papers dealing with an extensive class of anlytic difference operators admitting reflectionless eigenfunctions. In the first part, the pertinent difference operators and their reflectionless eigenfunctions are constructed from given "spectral data", in analogy with the IST for reflectionless Schrödinger and Jacobi operators. In the present paper, we introduce a suitable time dependence in the data, arriving at explicit solutions to a nonlocal evolution equation of Toda type, which may be viewed as an analog of the KdV and Toda lattice equations for the latter operators. As a corollary, we reobtain various known results concerning refletionless Schrödinger and Jacobi operators. Exploiting a reparametrization in terms of relativistic Calogero­Moser systems, we also present a detailed study of N-soliton solutions to our nonlocal evolution equation.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S.N.M. Ruijsenaars
PY  - 2001
DA  - 2001/05/01
TI  - Reflectionless Analytic Difference Operators II. Relations to Soliton Systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 256
EP  - 287
VL  - 8
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2001.8.2.8
DO  - 10.2991/jnmp.2001.8.2.8
ID  - Ruijsenaars2001
ER  -