Drift-induced Benjamin-Feir instabilities

TL;DR

This paper introduces a modified Ginzburg-Landau model with asymmetric couplings and drift, revealing a new class of Benjamin-Feir-like instabilities that lead to complex traveling and mosaic patterns.

Contribution

It presents a novel extension of the Ginzburg-Landau equation incorporating drift and asymmetry, uncovering new instability regimes beyond classical Benjamin-Feir conditions.

Findings

Drift induces Benjamin-Feir-like instabilities outside classical parameter regions.

Destabilization leads to traveling wave patterns or patchy mosaics.

Asymmetric coupling and drift are key to the observed pattern formations.

Abstract

A modified version of the Ginzburg-Landau equation is introduced which accounts for asymmetric couplings between neighbors sites on a one-dimensional lattice, with periodic boundary conditions. The drift term which reflects the imposed microscopic asymmetry seeds a generalized class of instabilities, reminiscent of the Benjamin-Feir type. The uniformly synchronized solution is spontaneously destabilized outside the region of parameters classically associated to the Benjamin-Feir instability, upon injection of a non homogeneous perturbation. The ensuing patterns can be of the traveling wave type or display a patchy, colorful mosaic for the modulus of the complex oscillators amplitude.