Advances in Differential Equations
- Adv. Differential Equations
- Volume 23, Number 11/12 (2018), 793-846.
Extension theory approach in the stability of the standing waves for the NLS equation with point interactions on a star graph
The aim of this work is to demonstrate the effectiveness of the extension theory of symmetric operators in the investigation of the stability of standing waves for the nonlinear Schrödinger equations with two types of non-linearities (power and logarithmic) and two types of point interactions ($\delta$- and $\delta'$-) on a star graph. Our approach allows us to overcome the use of variational techniques in the investigation of the Morse index for self-adjoint operators with non-standard boundary conditions which appear in the stability study. We also demonstrate how our method simplifies the proof of the stability results known for the NLS equation with point interactions on the line.
Adv. Differential Equations, Volume 23, Number 11/12 (2018), 793-846.
First available in Project Euclid: 25 September 2018
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 81Q35: Quantum mechanics on special spaces: manifolds, fractals, graphs, etc. 37K40: Soliton theory, asymptotic behavior of solutions 37K45: Stability problems 47E0
Pava, Jaime Angulo; Goloshchapova, Nataliia. Extension theory approach in the stability of the standing waves for the NLS equation with point interactions on a star graph. Adv. Differential Equations 23 (2018), no. 11/12, 793--846. https://projecteuclid.org/euclid.ade/1537840834