Cristina Sardón is a post doctoral student who recently defended her (international mention) doctoral thesis in our Department of Fundamental Physics in the University of Salamanca. Her research is rigorously mathematically well-founded. Her interests are focused on the geometric/algebraic interpretation of nonlinear phenomena and the integrability of differential equations appearing in Physics. In particular, the treatment of evolutionary waves in the realm of Fluid Dynamics, Optics, Solid State, among other scientific disciplines.
Her expertise in these fields has been achieved by supervision of P.G. Estévez, Full Professor of Theoretical Physics of this department and J. de Lucas, associate professor of the University of Warsaw, Poland, who has been her co-adviser. Her international doctorate mention has been awarded due to her multiple research stays abroad at the University of Warsaw in Poland with J. de Lucas or the University of Roma Tre in Rome, Italy.
She is part of the Geometry, Mechanics and Control network of which she is an active member through multiple seminars and editorial duties. Also, she has completed teaching tasks by teaching introductory courses of Differential Equations and Mechanics to undergraduates in their second year of their Grade in Physics at the University of Salamanca.
Currently, she is looking for a post doctoral position and opening new fields of research in the realm of discrete differential equations.
Nonlinear Dyn (2017) 87:13–23 (2017)''
Jacobi–Lie systems: Fundamentals and low-dimensional classification
Lie symmetries for Lie systems: Applications to systems of ODEs and PDEs
Applied Mathematics and Computation 273 - 435–452 (2015)''
Lie–Hamilton systems on the plane: Applications and superposition rules
PhD: Lie systems, lie symmetries and reciprocal transformations
Dirac–Lie systems and Schwarzian equations
Classification of Lie-hamilton systems on the plane.
J: of Physics A: Math. and Theor. (2013). (In press) (2013)''
From constant of motion to superposition rules of Lie Hamilton systems
J. Phys. A: Math. Theor. 46, 285203 (2013)''
Integrable 1+1 dimensional hierarchies arising from reduction of a non-isospectral problem in 2+1 dimensions
Appl. Mathematics. and Computation. 224, 311-324 (2013)''
Iterative symmetry search and reduction of a water wave model in 2 + 1 dimensions
Lie Hamilton systems: theory and applications
Int. Geom. Methods Mod. Phys.10, 09129823 (2013)''
Miura-reciprocal tansformations for non-isospectral Camassa-Holm hierarchies in 2+1 dimensions
Journal of Nonlinear Mathematical Physics 20, (2013). (In press) (2013)''
Miura-Reciprocal transformations for two integrable hierarchies in 1 + 1 dimensions
On Lie systems and Kummer-Schwarz equations
J. Math. Phys. 54, 033505 (2013)''
A new Lie systems approach to second-order Riccati equations
Int. J. Geom. Methods Mod. Phys. 9, 1260007 (2012)''
Non-isospectral 1+1 hierarchies arising from a Camassa-Holm Hierarchy in 2+1 dimensions
Journal of Nonlinear Math. Physics, 18, 9-28 (2011)''