Edge-localized states on quantum graphs in the limit of large mass

We construct and quantify asymptotically in the limit of large mass a variety of edge-localized stationary states of the focusing nonlinear Schrödinger equation on a quantum graph. The method is applicable to general bounded and unbounded graphs. The solutions are constructed by matching a localized large amplitude elliptic function on a single edge with an exponentially smaller remainder on the rest of the graph. This is done by studying the …