Non-reciprocal breathing solitons

TL;DR

This paper reports the experimental observation and theoretical analysis of long-lived, unidirectional breathing solitons in non-reciprocal, non-conservative active metamaterials, revealing new mechanisms for stable nonlinear wave propagation.

Contribution

It demonstrates the existence of unidirectional, long-lived breathing solitons in non-reciprocal active metamaterials through experiments, simulations, and theory, highlighting their stability conditions.

Findings

Breathing solitons can be unidirectional and long-lived in non-reciprocal materials.

Their dynamics are governed by an unstable fixed point with bifurcation conditions.

Discrete effects can enhance the stability of these breathers.

Abstract

Breathing solitons consist of a fast beating wave within a compact envelope of stable shape and velocity. They can propagate and carry information and energy in a variety of contexts such as plasmas, optical fibers and cold atoms, but propagating breathers have remained elusive when energy conservation is broken. Here, we report on the observation of breathing, unidirectional, arbitrarily long-lived solitons in non-reciprocal, non-conservative active metamaterials. Combining precision desktop experiments, numerical simulations and perturbation theory on generalizations of the sine-Gordon and nonlinear Schr\"odinger equations, we demonstrate that unidirectional breathers generically emerge in weakly nonlinear non-reciprocal materials, and that their dynamics are governed by an unstable fixed point. Crucially, breathing solitons can persist for arbitrarily long times provided: (i) this fixed point displays a bifurcation when a delicate balance between energy injection and dissipation is struck; (ii) the initial conditions allow the dynamics to reach this bifurcation point. Importantly, discrete effects tend to stabilize these non-reciprocal breathers over a wider range of initial conditions. Our work establishes non-reciprocity as a promising avenue to generate stable nonlinear unidirectional waves, and could be generalized beyond metamaterials to optics, soft matter and superconducting circuits.