Novikov equations with quadratic non-linearities: structural and qualitative properties

• Grant number: 20/02055-0
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2021
• End date: January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Igor Leite Freire
• Grantee: Igor Leite Freire
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

We aim at investigating structural and qualitative properties of equations with quadratic non-linear terms discovered by V. Novikov in 2009. From the structural point of view we are interested in the investigation of invariance, conservation laws and integrability. From the qualitative perspective our main interest relies on local and global existence of solutions, as well as the wave-breaking phenomenon. (AU)

Scientific publications

(7)

(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)

FREIRE, IGOR LEITE; TITO, RODRIGO DA SILVA. Novikov equation describing pseudo-spherical surfaces, its pseudo-potentials, and local isometric immersion. STUDIES IN APPLIED MATHEMATICS, v. 148, n. 2, OCT 2021. (20/02055-0)

FREIRE, IGOR LEITE. Persistence properties of a Camassa-Holm type equation with (n+1)-order non-linearities. Journal of Mathematical Physics, v. 63, n. 1, JAN 1 2022. (20/02055-0)

SALES FILHO, NAZIME; FREIRE, IGOR LEITE. Structural and qualitative properties of a geometrically integrable equation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 114, p. 13-pg., 2022-07-04. (20/02055-0)

FREIRE, IGOR LEITE. Geometrical demonstration for persistence properties of a bi-Hamiltonian shallow water system. Journal of Mathematical Physics, v. 63, n. 4, p. 10-pg., 2022-04-01. (20/02055-0)

DURUK MUTLUBAS, NILAY; FREIRE, IGOR LEITE. The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation. APPLICABLE ANALYSIS, v. N/A, p. 14-pg., 2022-04-01. (20/02055-0)

FREIRE, IGOR LEITE. Unique continuation results for abstract quasi-linear evolution equations in Banach spaces. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, v. 20, n. 3, p. 17-pg., 2023-01-01. (20/02055-0)

FREIRE, IGOR LEITE; TOFFOLI, CARLOS EDUARDO. Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations. Journal of Differential Equations, v. 358, p. 27-pg., 2023-02-22. (20/02055-0)