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Boundary triplet theory and its applications to spectral theory of differential operators with point interactions and nonlinear Schrödinger equations with potentials of $ / delta $ - $ delta $ type

Grant number: 12/50503-6
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): January 01, 2013
Effective date (End): November 25, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Jaime Angulo Pava
Grantee:Nataliia Goloshchapova
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project is principally aimed to demonstrate efficiency of boundary triplets and the corresponding Weyl functions approach for the investigation of certain spectral characteristics of differential operators with point interactions. We also plan to apply boundary triplets approach for investigation of non-linear Schrodinger equation with periodic and non-periodic $\delta$-potential and the problem of the existence and stability of standing waves for such non-linear Schrodinger models, i.e. stability study for the "standing-peak" solutions. The importance of investigation of such objects is due to their applications in quantum mechanics and Bose-Einstein condensates. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
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. Advances in Differential Equations, v. 23, n. 11-12, p. 793-846, NOV-DEC 2018. Web of Science Citations: 2.
PAVA, JAIME ANGULO; GOLOSHCHAPOVA, NATALIIA. Stability of standing waves for NLS-log equation with delta-interaction. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 24, n. 3 JUN 2017. Web of Science Citations: 6.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.