Discrete Nonlocal Nonlinear Schroedinger equation on Metric Graphs: Dynamics of PT-Symmetric Solitons in Discrete Networks

TL;DR

This paper investigates PT-symmetric discrete nonlocal nonlinear Schrödinger equations on metric graphs, deriving soliton solutions for simple topologies and demonstrating integrability through conservation laws.

Contribution

It introduces a novel analysis of PT-symmetric nonlocal nonlinear Schrödinger equations on metric graphs, including soliton solutions and proof of integrability.

Findings

Soliton solutions for star and tree graphs.

Proof of integrability via conservation laws.

Demonstration of PT-symmetry in discrete network models.

Abstract

We consider PT-symmetric, discrete nonlocal nonlinear Schr\"{o}dinger equation on metric graphs. Soliton solutions are obtained for simplest graph topologies, such as star and tree graphs. Integrability of the problem is shown by proving existence of infinite number of conservation laws.