Nonlinear waves in an anti-Hermitian lattice with cubic nonlinearity
Pattern Formation and Solitons
2020-01-08 v1 Exactly Solvable and Integrable Systems
Abstract
In an anti-Hermitian linear system, all energy eigenvalues are purely imaginary and the corresponding eigenvectors are orthogonal. This implies that no stationary state is available in such systems. We consider an anti-Hermitian lattice with cubic nonlinearity and explore novel nonlinear stationary modes. We discuss that relative population is conserved in a nonreciprocal tight binding lattice with periodical boundary conditions as opposed to parity-time (PT) symmetric lattices. We study nonlinear nonrecipocal dimer, triple and quadrimer models and construct stationary nonlinear modes.
Keywords
Cite
@article{arxiv.2001.02182,
title = {Nonlinear waves in an anti-Hermitian lattice with cubic nonlinearity},
author = {S. Tombuloglu and C. Yuce},
journal= {arXiv preprint arXiv:2001.02182},
year = {2020}
}