Dynamics of fronts in optical media with linear gain and nonlinear losses

TL;DR

This paper investigates the behavior of fronts in dispersive optical media with gain and nonlinear losses, revealing how initial conditions influence front parameters and identifying conditions for observing fronts.

Contribution

It demonstrates that front parameters depend on initial conditions and identifies a global bifurcation where solitons transition to fronts in such media.

Findings

Front velocity depends on initial conditions.

A global bifurcation replaces solitons with front solutions.

Front velocity must exceed modulational instability velocity.

Abstract

The dynamics of fronts, or kinks, in dispersive media with gain and losses is considered. It is shown that the front parameters, such as the velocity and width, depend on initial conditions. This result is not typical for dissipative systems. For exponentially decreasing initial conditions, the relations for the front parameters are found. A presence of the global bifurcation, when a soliton solution is replaced by the front solution, is demonstrated. It is also shown that in order to observe fronts, the front velocity should be larger than the characteristic velocity of the modulational instability.