Nonlinear supratransmission in multicomponent systems

TL;DR

This paper introduces a new method to determine the supratransmission threshold in complex multicomponent nonlinear systems, demonstrated on a three-wave interaction model where no analytic solutions exist.

Contribution

The paper presents a novel approach for calculating the supratransmission threshold in nonintegrable multicomponent nonlinear systems, applicable even when analytic solutions are unavailable.

Findings

Successfully applied to a three-wave resonant interaction model

Determined the supratransmission threshold without known analytic expressions

Demonstrated broad applicability to nonlinear systems

Abstract

A method is proposed to solve the challenging problem of determining the supratransmission threshold (onset of instability of harmonic boundary driving inside a band gap) in multicomponent nonintegrable nonlinear systems. It is successfully applied to the degenerate three-wave resonant interaction in a birefringent quadratic medium where the process generates spatial gap solitons. No analytic expression is known for this model showing the broad applicability of the method to nonlinear systems.