Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation

TL;DR

This paper investigates the behavior of channel-guided solitons in a two-dimensional nonlinear Schrödinger equation, focusing on their interactions, phase effects, and reflection phenomena at junctions.

Contribution

It provides new insights into soliton dynamics at junctions, including phase-induced Josephson oscillations and reflection conditions in a 2D nonlinear Schrödinger framework.

Findings

Two solitons merge without phase shift at junctions.

Phase difference induces Josephson oscillations.

Reflections occur below a critical velocity.

Abstract

Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. 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.