Quasinormal modes: mathematical and physical aspects

• Grant number: 25/07279-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2025
• End date: December 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Alberto Vazquez Saa
• Grantee: Thiago Henrique de Nadai
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This undergraduate research project proposes a theoretical and numerical study of quasinormal modes (QNMs), which are solutions to differential equations associated with open physical systems that exhibit energy dissipation. Traditionally employed in contexts such as General Relativity and the study of black holes, QNMs have gained increasing relevance in fields like optics and photonics, particularly in describing optical solitons in nonlinear media. The project aims to understand the application of this formalism to such systems by investigating the perturbation equation for solitons with third-order dispersion, deriving analytical solutions via the inverted Pöschl-Teller equation, performing numerical simulations of decay (ringdown), and exploring analogies with gravitational phenomena. (AU)