Advances in Differential Equations

Extension theory approach in the stability of the standing waves for the NLS equation with point interactions on a star graph

Jaime Angulo Pava and Nataliia Goloshchapova

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Abstract

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.

Article information

Source
Adv. Differential Equations, Volume 23, Number 11/12 (2018), 793-846.

Dates
First available in Project Euclid: 25 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.ade/1537840834

Mathematical Reviews number (MathSciNet)
MR3857871

Zentralblatt MATH identifier
06982200

Subjects
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

Citation

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


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