najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1174Research ArticleMATHEMATICSМАТЕМАТИКАNonlinearity-defect interaction: symmetry breaking bifurcation in a NLS with a 𝛿′ impurityAdamiR.

Riccardo Adami – Dipartimento di Matematica e Applicazioni, Assistant Professor

riccardo.adami@unimib.itNojaD.

Diego Noja – Dipartimento di Matematica e Applicazioni, Assistant Professor

diego.noja@unimib.itUniversit`a di Milano BicoccaItaly20111808202524519Copyright © Adami R., Noja D., 20252025Adami R., Noja D.Adami R., Noja D.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1174

We illustrate some new results and comment on perspectives of a recent research line, focused on the stability of stationary states of nonlinear NLS with point interactions. We describe in detail the case of a “𝛿′” interaction, that provides a rich model endowed with a pitchfork bifurcation with symmetry breaking in the family of ground states. Finally, we give a direct proof of the stability of the ground states in the cases of a subcritical and critical (in the sense of the blow-up) nonlinearity power. 

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The authors declare that there are no conflicts of interest present.