Standing waves on quantum graphs
Analysis of PDEs
2022-06-15 v1 Mathematical Physics
Dynamical Systems
math.MP
Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
Abstract
We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational theory, dynamical systems on a phase plane, and the Dirichlet-to-Neumann mappings.
Keywords
Cite
@article{arxiv.2201.08114,
title = {Standing waves on quantum graphs},
author = {Adilbek Kairzhan and Diego Noja and Dmitry E. Pelinovsky},
journal= {arXiv preprint arXiv:2201.08114},
year = {2022}
}
Comments
48 pages; 19 figures