| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 1
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| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 38, n. 10, p. 5039-5066, OCT 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
We study the nonlinear Schrodinger equation (NLS) 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 instability of the standing waves e(i omega t)Phi(x) of the NLS-delta equation with attractive power nonlinearity on G 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, avoiding the variational techniques standard in the stability study. We also prove the orbital stability of the unique standing wave solution to the NLS-delta equation with repulsive nonlinearity. (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 |