Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model

TL;DR

This paper investigates how near-PT symmetric potentials with spectral filtering and gain-loss parameters influence solitons in a complex Ginzburg-Landau model, revealing stable soliton regions and stability properties.

Contribution

It introduces the effects of near-PT symmetry on solitons in the CGL equation, identifying stable regions and stability spectra related to spectral filtering and gain-loss coefficients.

Findings

Most stable solitons exist in the second quadrant of the $(\alpha_2, \beta_2)$ space.

Certain symmetric points in parameter space have purely imaginary stability spectra.

Unstable modes can transition to stable modes via adiabatic parameter changes.

Abstract

We present and theoretically report the influence of a class of near-parity-time-(PT-) symmetric potentials with spectral filtering parameter $\alpha_2$ and nonlinear gain-loss coefficient $\beta_2$ on solitons in the complex Ginzburg-Landau (CGL) equation. The potentials do not admit entirely-real linear spectra any more due to the existence of coefficients $\alpha_2$ or $\beta_2$. However, we find that most stable exact solitons can exist in the second quadrant of the $(\alpha_2, \beta_2)$ space, including on the corresponding axes. More intriguingly, the centrosymmetric two points in the $(\alpha_2, \beta_2)$ space possess imaginary-axis (longitudinal-axis) symmetric linear-stability spectra. Furthermore, an unstable nonlinear mode can be excited to another stable nonlinear mode by the adiabatic change of $\alpha_2$ and $\beta_2$. Other fascinating properties associated with the exact solitons are also examined in detail, such as the interactions and energy flux. These results are useful for the related experimental designs and applications.