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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 Opportunities: 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 Host 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)