Soliton transport in tubular networks: transmission at vertices in the shrinking limit

TL;DR

This paper investigates how solitons propagate through tubular networks modeled as fat graphs, analyzing the effects of graph thickness and vertex angles on transmission and reflection, especially as the network's thickness approaches zero.

Contribution

It extends previous work by analyzing soliton transport on finite-thickness graphs and relates the results to the zero-thickness limit, highlighting conditions for reflectionless transmission.

Findings

Reflectionless vertex transmission occurs in the shrinking limit.

Wave function behavior depends on graph thickness and bond angles.

Reflection coefficients approach those of the zero-thickness case as thickness decreases.

Abstract

Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the angle between its bonds is studied and related to a special case considered in our previous work, in the limit when the thickness of the graph goes to zero. It is found that both the wave function and reflection coefficient reproduce the regime of reflectionless vertex transmission studied in our previous work.