Stability propertiesproperties of standing waves for NLS equations with the delta'-interaction

Author(s)

Pava, Jaime Angulo ^[1] ; Goloshchapova, Nataliia ^[1]

Affiliation

^[1] IME USP, Dept Math, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: PHYSICA D-NONLINEAR PHENOMENA; v. 403, FEB 2020.
• Web of Science Citations: 0

Abstract

We study the orbital stability of standing waves with discontinuous bump-like profile for the nonlinear Schrodinger model with the repulsive delta'-interaction on the line. We consider the model with power non-linearity. In particular, it is shown that such standing waves are unstable in the energy space under some restrictions for parameters. The use of extension theory of symmetric operators by Krein-von Neumann is fundamental for estimating the Morse index of self-adjoint operators associated with our stability study. Moreover, for this purpose we use Sturm oscillation results and analytic perturbation theory. The Perron-Frobenius property for the repulsive delta'-interaction is established. The arguments presented in this investigation have prospects for the study of the stability of stationary waves solutions of other nonlinear evolution equations with point interactions. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• FAPESP's process: 16/02060-9 - Application of the theory of extensions to the spectral analysis of some self-adjoint operators
• Grantee: Nataliia Goloshchapova
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/07311-0 - Schrodinger equations with point interactions and instability for the fractional Korteweg- de Vries equation
• Grantee: Jaime Angulo Pava
• Support Opportunities: Scholarships abroad - Research