Soliton transport in tubular networks: transmission at vertices in the   shrinking limit
  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. 
Hannes Uecker, Daniel Grieser, Zarif Sobirov, Doniyor Babajanov and   Davron Matrasulov
nlin.PS cond-mat.dis-nn math-ph math.MP