Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model. (arXiv:1802.00857v1 [nlin.PS])

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

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