English

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

R2 v1 2026-06-24T08:56:25.468Z