Hamiltonian formulation of the standard $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer
Exactly Solvable and Integrable Systems
2015-06-23 v1 Mathematical Physics
math.MP
Abstract
The standard -symmetric dimer is a linearly-coupled two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. We show that despite gain and loss, the standard -dimer is a Hamiltonian system. We also produce a Lagrangian formulation for the dimer.
Keywords
Cite
@article{arxiv.1410.3581,
title = {Hamiltonian formulation of the standard $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer},
author = {I. V. Barashenkov},
journal= {arXiv preprint arXiv:1410.3581},
year = {2015}
}
Comments
5 pages; presentation at the 3rd Dynamics Days South America (Vi\~na del Mar, Chile)