Higher order symmetries for linear and nonlinear Schroedinger equations
Abstract
We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases when these equations can be explicitly solved. In addition, the complete group classification of the nonlinear Schr\"odinger equation is presented.
Cite
@article{arxiv.1603.01715,
title = {Higher order symmetries for linear and nonlinear Schroedinger equations},
author = {A. G. Nikitin},
journal= {arXiv preprint arXiv:1603.01715},
year = {2016}
}
Comments
It is the preprint version of the contribution to the CRM Proceedings where the misprints are corrected and a half page text is added on Page 3. Tis publication is stimulated by the current interest in higher and arbitrary order integrals of motion. The determining equations for just such integrals, valid for arbitrary number of independent variables are the main subject of this preprint