Breather Solutions to a Two-dimensional Nonlinear Schr\"odinger Equation with Non-local Derivatives
Pattern Formation and Solitons
2022-09-20 v1
Abstract
We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity levels. With the increase of nonlinearity, the breathers break down, giving way to wave turbulence (or Rayleigh-Jeans) spectra. Phase-space trajectories associated with the breather solutions are found to be close to that of the linear system, revealing a connection between the breather solution and Kolmogorov-Arnold-Moser (KAM) theory.
Keywords
Cite
@article{arxiv.2209.08155,
title = {Breather Solutions to a Two-dimensional Nonlinear Schr\"odinger Equation with Non-local Derivatives},
author = {Alexander Hrabski and Yulin Pan},
journal= {arXiv preprint arXiv:2209.08155},
year = {2022}
}