On the standing waves of the NLS-log equation with a point interaction on a star graph

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Goloshchapova, Nataliia¹ 

[1] Univ Sao Paulo, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

关键词: Logarithmic nonlinearity;    Nonlinear Schrodinger equation;    Orbital stability;    Spectral instability;    Standing wave;    Star graph;   

DOI  :  10.1016/j.jmaa.2018.12.019

来源: Elsevier

【 摘 要 】

We study the nonlinear Schrodinger equation with logarithmic nonlinearity on a star graph g. At the vertex an interaction occurs described by a boundary condition of delta type with strength alpha is an element of R. We investigate the orbital stability and the spectral instability of the standing wave solutions e(i omega t)Phi(x) to the equation when the profile Phi(x) has mixed structure (i.e. has bumps and tails). In our approach we essentially use the extension theory of symmetric operators by Krein-von Neumann, and the analytic perturbations theory. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free