Standing waves on a flower graph

A flower graph consists of a half line and N symmetric loops connected at a single vertex with N ≥ 2 (it is called the tadpole graph if N = 1 ). We consider positive single-lobe states on the flower graph in the framework of the cubic nonlinear Schrödinger equation. The main novelty of our paper is a rigorous application of the period function for second-order differential equations towards understanding the symmetries and bifurcations of …