A Note on Sign-Changing Solutions to the NLS on the Double-Bridge Graph

Abstract

We study standing waves of the NLS equation posed on the double-bridge graph: two semi-infinite half-lines attached at a circle. At the two vertices, Kirchhoff boundary conditions are imposed. We pursue a recent study concerning solutions nonzero on the half-lines and periodic on the circle, by proving some existing results of sign-changing solutions non-periodic on the circle.

Keywords

• quantum graphs
• non-linear Schrödinger equation
• standing waves