Variational methods and stability of periodic waves for nonlinear dispersive systems

• Grant number: 17/20760-0
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): April 01, 2018
• Effective date (End): March 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Ademir Pastor Ferreira
• Grantee: Fabrício Cristófani
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project aims to establish a variational criterion for obtaining periodic solutions as well as sufficient conditions for the orbital stability of periodic traveling waves associated with dispersive systems. The periodic traveling waves we are interested in is the ones propagating at constant speed. In order to conclude the stability result, we will use a new approach that deals with defining a new Lyapunov functional for the orbit generated by the periodic wave. Our objective is to show that, depending on the linearized operator, this particular class of systems always have orbitally stable periodic waves.

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)

CRISTOFANI, FABRICIO; PASTOR, ADEMIR. NONLINEAR STABILITY OF PERIODIC-WAVE SOLUTIONS FOR SYSTEMS OF DISPERSIVE EQUATIONS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 19, n. 10, p. 5015-5032, OCT 2020. Web of Science Citations: 0.

CRISTOFANI, FABRICIO; NATALI, FABIO; PASTOR, ADEMIR. PERIODIC TRAVELING-WAVE SOLUTIONS FOR REGULARIZED DISPERSIVE EQUATIONS: SUFFICIENT CONDITIONS FOR ORBITAL STABILITY WITH APPLICATIONS. COMMUNICATIONS IN MATHEMATICAL SCIENCES, v. 18, n. 3, p. 613-634, 2020. Web of Science Citations: 1.

ALMEIDA, GISELE DETOMAZI; CRISTOFANI, FABRICIO; NATALI, FABIO. On the stability of periodic traveling waves for the modified Kawahara equation. APPLICABLE ANALYSIS, AUG 2019. Web of Science Citations: 1.