Reflection of Channel-Guided Solitons at Corners and Junctions in Two-Dimensional Nonlinear Schrödinger Equation

Solitons confined in channels are studied in the two-dimensional nonlinear Schrödinger equation. First, we study a channel-guided soliton in a curved channel. The channel-guided soliton can go through a hairpin curve fairly easily, whereas it can be reflected at a right-angle corner. We find that chaotic scattering is involved with the transition between transmission and reflection. Next, we study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one soliton, when there is no phase shift. If a phase difference is given to the two solitons, the Josephson oscillation is induced. The Josephson oscillation is amplified near the junction. The two solitons are reflected when the initial velocity is below a critical value.