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

Soliton transport in tubelike networks is studied by solving the nonlinear Schrödinger 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.