Dynamics for Schrodinger and Korteweg-de Vries-type models on quantum graphs

• Grant number: 24/20623-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2025
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Jaime Angulo Pava
• Grantee: Alexander Muñoz Garcia
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This project is devoted to the study of the Airy and Schrödinger operators on metric graphs involving several amount of half-lines attached to a common vertex. We consider the case of an extra terminal vertex (i.e. a T -shaped graph) and the case of a loop structure attached to the common vertex (known as looping-edge graph). In such contexts, the goal of this research project is, mainly, to study the existence and (in)stability of stationary solutions of Korteweg-de Vries equations and standing waves for non-linear Schrödinger-type equations, as well as, the Cauchy problem of these models on looping-edgegraphs