Energy flow of moving dissipative topological solitons

TL;DR

This paper investigates the detailed energy flow mechanisms of moving topological solitons in nonlinear systems, revealing an additional exchange energy flux channel that is crucial for understanding energy transfer, especially under AC driving forces.

Contribution

It identifies and analyzes an exchange energy flux channel mediated by system inhomogeneity, which is essential for understanding soliton energy flow under various external forces.

Findings

The exchange energy flux channel is small but non-zero under DC driving.

Under AC driving, the exchange flux mediates the entire energy flow.

Spatial discretization effects influence the energy flow dynamics.

Abstract

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a DC external force the corresponding exchange current is shown to be small but non-zero. For the case of AC driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of AC and DC external forces, as well as spatial discretization effects.