Reflection and Splitting of Channel-Guided Solitons in Two-dimensional Nonlinear Schr\"odinger Equation

TL;DR

This paper investigates how channel-guided solitons in a 2D nonlinear Schrödinger equation split or reflect at a branching point, providing a variational method to predict critical energy for splitting and aiding channel system design.

Contribution

The study introduces a variational approach to determine the critical kinetic energy for soliton splitting at channel bifurcations in 2D nonlinear Schrödinger systems.

Findings

Solitons split when initial kinetic energy exceeds a critical value.

Below the critical energy, solitons are reflected at the branching point.

The variational method effectively predicts the critical energy for splitting.

Abstract

Solitons confined in a channel are studied in the two-dimensional nonlinear Schroedinger equation. When a channel branches into two channels, a soliton is split into two solitons, if the initial kinetic energy exceeds a critical value. The branching point works as a pulse splitter. If it is below the critical value, the soliton is reflected. The critical kinetic energy for splitting is evaluated by a variational method. The variational method can be applied in the design of channel systems with reduced reflection.