Last update: 18/02/2021
We are interested to the geometric study of differential equations in the framework of the theory of jet spaces, and to its interplays with problems of differential geometry and mathematical physics.
Researchers:
Diego Catalano Ferraioli (UFBA) - Principal investigator
Students:
Geometry of nonlinear differential equations
Principal investigator: Diego Catalano Ferraioli (UFBA)
Funding Agency: CNPq
Further details: This is a CNPq "Universal project" that aims at the following objectives: new results on the reduction and integration methods, with particular attention to the methods that make use of symmetries (local and nonlocal) and of Darboux, Bäcklund and reciprocal transformations; study and classification of the equations that admit zero-curvature representations, with particular attention to the equations that describe pseudo-spherical surfaces; application of differential invariant theory in the study and classification of integrable equations; applications of the classical theory of surface transformations to the study of the integrability of differential equations.
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Geometric methods for the study and reduction of nonlinear differential equations
Principal investigator: Diego Catalano Ferraioli (UFBA)
Funding Agency: CNPq Fellowship of Research Productivity
Further details: The main objective of the project is the study of the geometry of nonlinear differential equations, by giving continuity to some of our previous research on the study and classification of special classes of equations and the problem of integration and reduction. In particular, the project will focus on the following two main aspects: the study and classification of equations that admit zero-curvature representations, with particular attention to the equations that describe pseudo-spherical surfaces; application of the theory of differential invariants in the study and classification of integrable equations.
D. CATALANO FERRAIOLI, T. CASTRO SILVA and K. TENENBLAT. A note on isometric immersions and differential equations which describe pseudospherical surfaces (2019)
arXiv:1910.14523
D. CATALANO FERRAIOLI, T. CASTRO SILVA and K. TENENBLAT. A class of quasilinear second order partial differential equations which describe spherical or pseudospherical surfaces. JOURNAL OF DIFFERENTIAL EQUATIONS, v. 268, p. 7164-7182, 2019
D. CATALANO FERRAIOLI and DE OLIVEIRA SILVA, L.A. . Second order evolution equations which describe pseudospherical surfaces. Journal of Differential Equations (Print), v. 260, p. 8072-8108, 2016
D. CATALANO FERRAIOLI and DE OLIVEIRA SILVA, L.A. . Local isometric immersions of pseudospherical surfaces described by evolution equations in conservation law form. Journal of Mathematical Analysis and Applications (Print), v. 446, p. 1606-1631, 2016, 2016
D. CATALANO FERRAIOLI and DE OLIVEIRA SILVA, L.A. . Local isometric immersions of pseudospherical surfaces described by evolution equations in conservation law form. Journal of Mathematical Analysis and Applications (Print), v. 446, p. 1606-1631, 2016, 2016
D. CATALANO FERRAIOLI and L. A. de OLIVEIRA SILVA, Nontrivial 1-parameter families of zero-curvature representations via symmetry actions, J. Geometry and Physics, v. 94, p. 185-198, 2015
D. CATALANO FERRAIOLI and K. TENENBLAT, Fourth order evolution equations which describe pseudospherical surfaces, J. Differential Equations, v. 257, p. 3165-3199, 2014
D. CATALANO FERRAIOLI and M. MARVAN. The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors. ANNALI DI MATEMATICA PURA ED APPLICATA, v. 199, p. 1343-1380, 2020.
D. CATALANO FERRAIOLI and A. M. Vinogradov, Differential invariants of generic parabolic Monge Ampere equations, Journal of Physics. A, Mathematical and Theoretical (Print), v. 45, p. 265204, 2012
D. CATALANO FERRAIOLI and G. Gaeta. On the geometry of twisted symmetries: Gauging and coverings. JOURNAL OF GEOMETRY AND PHYSICS, v. 151, p. 103620, 2020.
D. CATALANO FERRAIOLI and P. MORANDO, Integration of Some Examples of Geodesic Flows via Solvable Structures, Journal of Nonlinear Mathematical Physics, v. 21, p. 521-532, 2014
D. CATALANO FERRAIOLI and P. Morando, Local and nonlocal solvable structures in the reduction of ODEs, Journal of Physics. A, Mathematical and Theoretical (Print), v. 42, p. 035210, 2009
D. CATALANO FERRAIOLI and P. MORANDO, APPLICATIONS OF SOLVABLE STRUCTURES TO THE NONLOCAL SYMMETRY-REDUCTION OF ODEs, Journal of Nonlinear Mathematical Physics (Print), v. 16, p. 27, 2009
D. CATALANO FERRAIOLI, Nonlocal aspects of lambda-symmetries and ODEs reduction, Journal of Physics. A, Mathematical and Theoretical, v. 40, p. 5479-5489, 2007
D. CATALANO FERRAIOLI and P. Morando, SYMMETRIES AND FIRST INTEGRALS FOR NON-VARIATIONAL EQUATIONS, International Journal of Geometric Methods in Modern Physics, v. 04, p. 1217, 2007
D. CATALANO FERRAIOLI, G. Manno and F. Pugliese, Generalised symmetries of partial differential equations via complex transformations, Bulletin of the Australian Mathematical Society, v. 76, p. 243-262, 2007
D. CATALANO FERRAIOLI and A. M. Vinogradov, Ricci flat 4-metrics with bidimensional null orbits. I. General aspects and nonabelian case., Acta Applicandae Mathematicae, v. 92, p. 209-225, 2006
D. CATALANO FERRAIOLI and A. M. Vinogradov, Ricci flat 4-metrics with bidimensional null orbits. II. The abelian case, Acta Applicandae Mathematicae, v. 92, p. 226-239, 2006
D. CATALANO FERRAIOLI, G. Manno and F. Pugliese, Contact symmetries of the elliptic Euler-Darboux equation, Note di Matematica. Università Degli Studi di Lecce, v. 23, p. 3-14, 2004
Designed and mantained by Diego Catalano Ferraioli