Orbital stability of standing waves for supercritical NLS with potential on graphs

TL;DR

This paper investigates the existence and orbital stability of standing waves in supercritical nonlinear Schrödinger equations with potentials on starlike graphs, extending stability results to more complex graph structures.

Contribution

It establishes the existence and orbital stability of normalized standing waves for supercritical NLS with potentials on general starlike graphs, under broad conditions.

Findings

Existence of orbitally stable standing waves in supercritical regimes.

Stability results applicable to general starlike graphs.

Extension of stability theory to NLS with potentials on graphs.

Abstract

In this paper we study the existence and stability of normalized standing waves for the nonlinear Schr\"odinger equation on a general starlike graph with potentials. Under general assumptions on the graph and the potential, we show the existence of orbitally stable standing waves when the nonlinearity is $L^{2}$-critical and supercritical.