Symmetries for exact solutions to the nonlinear Schr\"odinger equation
Exactly Solvable and Integrable Systems
2010-03-15 v1
Abstract
A certain symmetry is exploited in expressing exact solutions to the focusing nonlinear Schr\"odinger equation in terms of a triplet of constant matrices. Consequently, for any number of bound states with any number of multiplicities the corresponding soliton solutions are explicitly written in a compact form in terms of a matrix triplet. Conversely, from such a soliton solution the corresponding transmission coefficients, bound-state poles, bound-state norming constants and Jost solutions for the associated Zakharov-Shabat system are evaluated explicitly. It is also shown that these results hold for the matrix nonlinear Schr\"odinger equation of any matrix size.
Cite
@article{arxiv.0905.4231,
title = {Symmetries for exact solutions to the nonlinear Schr\"odinger equation},
author = {Tuncay Aktosun and Theresa Busse and Francesco Demontis and Cornelis van der Mee},
journal= {arXiv preprint arXiv:0905.4231},
year = {2010}
}