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.

COMMUNICATED BY:

• Siegfried Carl

KEYWORDS:

• Nonlinear Schrödinger equation
• quantum graphs
• standing waves
• stability

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 76B25
• 35Q51
• 35Q55
• 35R02

Acknowledgments

The author wishes to express their sincere thanks to the referees for his/her valuable comments that help to improve the main results of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.