English

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 PT\mathcal{PT}-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 PT\mathcal{PT}-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)