Lax hierarchy, Solitons, Sumrules and a dual Lax hierarchy
Abstract
It is shown that a set of functions which characterise the Lax hierarchy of non-linear equations may be represented in terms of the eigenstates of the potential which satisfies the generalised KdV equation. Such a representation leads to sumrules relating integrals involving the soliton potential and its various derivatives to sums involving the boundstate eigenvalues of the Schroedinger equation for the reflectionless potential. A new hierarchy of functions, which is in a sense dual to the Lax hierarchy, is identified. It is shown that time dependent equations involving the dual functions may be established which permit solutions related to an N-soliton structure similar to that for the Lax hierarchy but with a different 'speed' for the solitons.
Keywords
Cite
@article{arxiv.1206.5978,
title = {Lax hierarchy, Solitons, Sumrules and a dual Lax hierarchy},
author = {C. V. Sukumar},
journal= {arXiv preprint arXiv:1206.5978},
year = {2018}
}
Comments
17 pages. Typographical mistakes in the earlier version are corrected