Nonlocal Nonlinear Schrodinger Equation on Metric Graphs

TL;DR

This paper studies a PT-symmetric nonlocal nonlinear Schrödinger equation on metric graphs, deriving boundary conditions, finding soliton solutions for simple topologies, and proving integrability through conservation laws.

Contribution

It introduces a novel nonlocal nonlinear Schrödinger model on metric graphs, derives boundary conditions, and demonstrates integrability and soliton solutions for basic graph structures.

Findings

Derived vertex boundary conditions from conservation laws

Obtained explicit soliton solutions for star and tree graphs

Proved integrability via infinite conservation laws

Abstract

We consider PT-symmetric, nonlocal nonlinear Schrodinger equation on metric graphs. Vertex boundary conditions are derived from the conservation laws. 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.