Standing waves on a flower graph

A flower graph consists of a half line and N symmetric loops connected at single vertex with N≥2 (it is called the tadpole if N=1). We consider positive single-lobe states on in framework cubic nonlinear Schrödinger equation. The main novelty our paper rigorous application period function for second-order differential equations towards understanding symmetries bifurcations standing waves metric graphs. show that state (which ground energy small fixed mass) undergoes exactly one bifurcation larger mass, which point (N−1) branches other appear: each branch has K components (N−K) smaller components, where 1≤K≤N−1. only K=1 represents local minimizer large however, not attained mass N≥2. Analytical results obtained from are illustrated numerically.