Symmetries of the Hirota Difference Equation
Exactly Solvable and Integrable Systems
2017-07-10 v2
Abstract
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of their parameters as "times" of the nonlinear integrable partial differential-difference and differential equations. Examples of equations resulting in such procedure and their Lax pairs are given. Besides these, ordinary, symmetries the additional ones are introduced and their action on the Scattering data is presented.
Keywords
Cite
@article{arxiv.1704.00043,
title = {Symmetries of the Hirota Difference Equation},
author = {Andrei K. Pogrebkov},
journal= {arXiv preprint arXiv:1704.00043},
year = {2017}
}