Hirota difference equation: IST, Darboux transformation and solitons
Exactly Solvable and Integrable Systems
2015-06-22 v2 Mathematical Physics
math.MP
Abstract
Direct and inverse problems for the Hirota difference equation are considered. Jost solutions and scattering data are introduced and their properties are presented. Darboux transformation in a special case is shown to give evolution with respect to discrete time and a recursion procedure for consequent construction of the Jost solution at arbitrary time, if the initial value is given. Some properties of the soliton solutions are discussed.
Cite
@article{arxiv.1407.0677,
title = {Hirota difference equation: IST, Darboux transformation and solitons},
author = {Andrei Pogrebkov},
journal= {arXiv preprint arXiv:1407.0677},
year = {2015}
}
Comments
17 pages