Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction

TL;DR

This paper demonstrates stable long-distance propagation and on-off switching of colliding soliton sequences using a dissipative nonlinear Schrödinger model, supported by a Lotka-Volterra framework, with potential extensions to other solitary wave systems.

Contribution

It introduces a novel approach combining LV models and NLS equations to achieve stable soliton propagation and switching outside perturbative regimes.

Findings

Stable long-distance propagation across various gain-loss parameters.

Robust on-off and off-on switching via gain and loss ratio adjustments.

Extension of the LV-soliton dynamics relation to periodic phase sequences.

Abstract

We study propagation and on-off switching of two colliding soliton sequences in the presence of second-order dispersion, Kerr nonlinearity, linear loss, cubic gain, and quintic loss. Employing a Lotka-Volterra (LV) model for dynamics of soliton amplitudes along with simulations with two perturbed coupled nonlinear Schr\"odinger (NLS) equations, we show that stable long-distance propagation can be achieved for a wide range of the gain-loss coefficients, including values that are outside of the perturbative regime. Furthermore, we demonstrate robust on-off and off-on switching of one of the sequences by an abrupt change in the ratio of cubic gain and quintic loss coefficients, and extend the results to pulse sequences with periodically alternating phases. Our study significantly strengthens the recently found relation between collision dynamics of sequences of NLS solitons and population dynamics in LV models, and indicates that the relation might be further extended to solitary waves of the cubic-quintic Ginzburg-Landau equation.