ON THE ORBITAL INSTABILITY OF EXCITED STATES FOR THE NLS EQUATION WITH THE delta-INTERACTION ON A STAR GRAPH

Autor(es)

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

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 38, n. 10, p. 5039-5066, OCT 2018.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 16/02060-9 - Aplicação da teoria das extensões à análise espectral dos alguns operadores auto-adjuntos
• Beneficiário: Nataliia Goloshchapova
• Modalidade de apoio: Auxílio à Pesquisa - Regular