Solitary synchronization waves in distributed oscillators populations

TL;DR

This paper demonstrates the existence of solitary waves of synchrony in one-dimensional arrays of identical oscillators with Laplacian coupling, extending to non-identical oscillators with dissipative solitons.

Contribution

It introduces the concept of solitary synchronization waves in oscillator arrays and derives their solutions both analytically and numerically.

Findings

Existence of solitary waves of synchrony in identical oscillators.

Extension to dissipative solitons in non-identical oscillators.

Analytical and numerical characterization of these waves.

Abstract

We demonstrate existence of solitary waves of synchrony in one-dimensional arrays of identical oscillators with Laplacian coupling. Coarse-grained description of the array leads to nonlinear equations for the complex order parameter, in the simplest case to lattice equations similar to those of the discrete nonlinear Schrodinger lattice. Close to full synchrony, we find solitary waves for the order parameter perturbatively, starting from the known phase compactons and kovatons; these solution are extended numerically to the full domain of possible synchrony levels. For non-identical oscillators, existence of dissipative solitons is demonstrated.