Solitonic fixed point attractors in the complex Ginzburg-Landau equation for associative memories

TL;DR

This paper demonstrates that the complex Ginzburg-Landau equation with specific dissipative effects admits stable solitonic solutions acting as attractors, which can be used for associative memory models.

Contribution

It extends previous work by analyzing a more complex CGLE with two-photon absorption and quintic effects, establishing solitonic attractors as robust memory-like states.

Findings

Solitonic fixed points serve as attractors in the CGLE.

Amplitude and velocity of attractors are unaffected by quintic effects.

Two-photon absorption enhances the strength of the solitonic attractors.

Abstract

It was recently shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, \textit{Adv. Quantum Technol.} \textbf{2019} \textit{2}, 1800087] that the nonlinear Schrodinger equation with a simplified dissipative perturbation of special kind features a zero-velocity solitonic solution of non-zero amplitude which can be used in analogy to attractors of Hopfield's associative memory. In this work, we consider a more complex dissipative perturbation adding the effect of two-photon absorption and the quintic gain/loss effects that yields formally the complex Ginzburg-Landau equation (CGLE). We construct a perturbation theory for the CGLE with a small dissipative perturbation and define the behavior of the solitonic solutions with parameters of the system and compare the solution with numerical simulations of the CGLE. We show that similarly to the nonlinear Schrodinger equation with a simplified dissipation term, a zero-velocity solitonic solution of non-zero amplitude appears as an attractor for the CGLE. In this case the amplitude and velocity of the solitonic fixed point attractor does not depend on the quintic gain/loss effects. Furthermore, the effect of two-photon absorption leads to an increase in the strength of the solitonic fixed point attractor.