Ground States for NLS on Graphs: a Subtle Interplay of Metric and Topology

DOI10.1051/mmnp/201611202zbMath1390.35315arXiv1510.00818OpenAlexW2963441306MaRDI QIDQ4607483

Riccardo Adami

Publication date: 14 March 2018

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.00818

zbMATH Keywords

nonlinear Schrödinger equationgraphsground states

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (6)

Standing waves on quantum graphs ⋮ Index theorems for graph-parametrized optimal control problems ⋮ Classification and stability of positive solutions to the NLS equation on the T -metric graph ⋮ Edge-localized states on quantum graphs in the limit of large mass ⋮ Surgery principles for the spectral analysis of quantum graphs ⋮ Existence of the ground state for the NLS with potential on graphs

Cites Work

• Threshold phenomena and existence results for NLS ground states on metric graphs
• Constrained energy minimization and orbital stability for the NLS equation on a star graph
• NLS ground states on graphs
• NLS ground states on metric graphs with localized nonlinearities
• Variational properties and orbital stability of standing waves for NLS equation on a star graph
• Hilbert space operators in quantum physics
• Extremal properties of eigenvalues for a metric graph.
• On the inverse scattering method for integrable PDEs on a star graph
• Ground State on the Dumbbell Graph
• On the structure of critical energy levels for the cubic focusing NLS on star graphs
• Bifurcations and stability of standing waves in the nonlinear Schrödinger equation on the tadpole graph
• Nonlinear Schrödinger equation on graphs: recent results and open problems
• FAST SOLITONS ON STAR GRAPHS
• Existence of dynamics for a 1D NLS equation perturbed with a generalized point defect
• Ground state and orbital stability for the NLS equation on a general starlike graph with potentials
• Quantum graphs: I. Some basic structures
• Quantum fields on star graphs
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Ground States for NLS on Graphs: a Subtle Interplay of Metric and Topology