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

Abstract

In this paper we study the existence and stability of normalized standing waves for the nonlinear Schrödinger 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.

References in corpus (6)

• Existence and Stability of standing waves for supercritical NLS with a Partial Confinement
• Negative energy ground states for the $L^2$-critical NLSE on metric graphs
• Fast solitons on star graphs
• Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
• Soliton transport in tubular networks: transmission at vertices in the shrinking limit
• Stability of ground states for logarithmic Schrödinger equation with a ${\delta }^{\prime }$-interaction

Cited by in corpus (1)

• Standing waves on quantum graphs