NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2011, 2 (4), P. 5–19
NONLINEARITY-DEFECT INTERACTION:
SYMMETRY BREAKING BIFURCATION IN A NLS WITH A δ́ IMPURITY
Riccardo Adami – Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Italy, Assistant Professor, riccardo.adami@unimib.it.
Diego Noja – Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Italy, Assistant Professor, diego.noja@unimib.it.
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 ” δ́ ” 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.
Keywords: nonlinear dynamics, quantum mechanics, solitons, symmetry breaking, pitchfork bifurcation.
UDC 517.958
PACS 05.45.-a, 03.65.-W, 05.45.Yv