Schrodinger equations with point interactions and instability for the fractional Korteweg- de Vries equation

• Grant number: 16/07311-0
• Support Opportunities: Scholarships abroad - Research
• Effective date (Start): August 20, 2016
• Effective date (End): February 19, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jaime Angulo Pava
• Grantee: Jaime Angulo Pava
• Host Investigator: Jean-Claude Saut
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Research place: Université Paris-Sud (Paris 11), France

Abstract

The aim of this research project is the qualitative study of Schrodinger type models with points interaction determined by the delta distribution of Dirac or its derivative, as well as the study of the fractional Korteweg-de Vries equation. These research topics fit within the area of non-linear dispersive equations. Our research will be directed to the existence and stability or instability of traveling waves solutions and to the Cauchy problem, among others.These specific models are of recent research from a physical point of view in non-linear optics, propagation of optical beams in non-canonical means and graphs (for the Schrodinger type models) and water wave theory (for models type Korteweg-de Vries). The proposed research topic and the specific models being considered, in general, has been little development from the mathematical point of view. Several recent results in this topic have been obtained by the applicant and its collaborators as well as the associated scholarship supervisor that is being claimed (Prof. J-C Saut). In the case of Schrodinger type models with points of interaction, the applicant has used the extension theory for symmetric operators of Krein & von Neumann to simplify and extend recent results. For the well-posedness Cauchy problem associated with these models, we are interested in obtaining results of existence of solutions, uniqueness and continuous dependence of the solutions with respect to the initial data. (AU)

Scientific publications

(4)

(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; SAUT, JEAN-CLAUDE. EXISTENCE OF SOLITARY WAVE SOLUTIONS FOR INTERNAL WAVES IN TWO-LAYER SYSTEMS. QUARTERLY OF APPLIED MATHEMATICS, v. 78, n. 1, p. 75-105, MAR 2020. (16/07311-0)

PAVA, JAIME ANGULO; GOLOSHCHAPOVA, NATALIIA. Stability propertiesproperties of standing waves for NLS equations with the delta'-interaction. PHYSICA D-NONLINEAR PHENOMENA, v. 403, FEB 2020. (16/02060-9, 16/07311-0)

PAVA, JAIME ANGULO. Stability properties of solitary waves for fractional KdV and BBM equations. Nonlinearity, v. 31, n. 3, p. 920-956, MAR 2018. (16/07311-0)

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. (16/02060-9, 12/50503-6, 16/07311-0)