Publications

 

IN JOURNALS

  • Similarity reductions arising from nonisospectral Camassa Holm hierarchy in 2+1 dimensions.
    P.G. Estévez, J.D. Lejarreta, C. Sardón.
    J. of Nonlin. Math. Phys. 18,  9–28 (2011).
    arXiv:1506.07434
  • A new Lie systems approach to second-order Riccati equations.                                                                                            J.F. Cariñena, J. de Lucas, C. Sardón,                                                                                                                                      Int. J. Geom. Methods Mod. Phys. 9 , 1260007, (2012).                                                                                   arXiv:1110.3298
  • Miura reciprocal transformations for hierarchies in 2+1 dimensions.                                                                                     P.G. Estévez, C. Sardón,                                                                                                                                                              J. Nonlin. Math. Phys. 20, 552–564 (2013).                                                                                                   arXiv:1506.07434
  • Integrable 1+1 dimensional hierarchies arising from reduction of a non-isospectral problem in 2+1 dimensions.                  P.G. Estévez, J.D. Lejarreta, C. Sardón,                                                                                                                               Appl. Math.  Comput224, 311–324 (2013).                                                                                                   arXiv:1508.00561
  • On Lie systems and Kummer-Schwarz equations.                                                                                                                     J. de Lucas and C. Sardón                                                                                                                                                         J. Math. Phys. 54, 033505 (2013).                                                                                                                    arXiv:1212.5779
  • From constants of motion to superposition rules of Lie Hamilton systems.                                                                              A. Ballesteros, J.F. Cariñena, F.J. Herranz,  J. de Lucas, C. Sardón.                                                                                   J. Phys.A: Math. Theor.  46, 285203 (2013).                                                                                                        arXiv:1305.6272
  • Lie–Hamilton systems: theory and applications.                                                                                                                      J.F. Cariñena, J. de Lucas, C. Sardón.                                                                                                                                     Int. Geom. Methods Mod. Phys. 10, 09129823 (2013).                                                                                      arXiv:1211.6991
  • Lie-Hamilton systems on the plane: properties, classification and applications.                                                                         A. Ballesteros, A.Blasco, J.F. Cariñena, F.J. Herranz, J. de Lucas, C. Sardon.                                                                          J. Differential Equations 258, 2873–2907 (2015).                                                                                                              arXiv: 1311.0792
  • Lie–Dirac systems and Schwarzian equations.                                                                                                                       J.F. Cariñena, J. Grabowski, J. de Lucas, C. Sardón.                                                                                                                J. Differential Equations  257, 2303–2340 (2014).                                                                                               https://arxiv.org/abs/1305.6276
  • Lie symmetries for Lie systems: applications to systems of ODEs and PDEs.                                                                        P.G. Estévez, F.J. Herranz, J. de Lucas and C. Sardón.                                                                                                                Appl. Math. Comput. 273, 435–472 (2016).
    arXiv:1404.2740.
  • Lie–Hamilton systems on the plane: applications and superposition rules.                                                                               A. Blasco, F.J. Herranz, J. de Lucas, C. Sardón.                                                                                                                       J. Phys. A: Math. Theor. 48 , 345202 (2015).                                                                                                    arXiv:1410.7336.
  • Iterative symmetry search and reduction of a water wave model in 2+1 dimensions.                                                             P.G. Estévez, J.D. Lejarreta, C. Sardón,                                                                                                                           Nonlinear Dyn. 87, 13–23 (2017) .                                                                                                                        http://arxiv.org/pdf/1510.04962.pdf
  • A geometric Hamilton–Jacobi theory for a Nambu–Poisson structure.                                                                                   M. de León,  C. Sardón,                                                                                                                                                               J. Math. Phys.  58, 033508 (2017).                                                                                                                          https://arxiv.org/abs/1604.08904
  • Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems,                                     M. de León, C. Sardón,                                                                                                                                                  Accepted in J. Phys. A  (2017).                                                                                                                             https://arxiv.org/abs/1612.06224
  • Geometry of the discrete Hamilton–Jacobi equation. Applications in optimal control”                                                            M. de León, C. Sardón,                                                                                                                                                          Sent to Reports on Mathematical Physics (2017).                                                                                                      https://arxiv.org/abs/1704.04907
  • A geometric Hamilton–Jacobi theory on a Nambu–Jacobi manifold.                                                                                      M. de León. C. Sardón.                                                                                                                                                            Int. J. Geom. Methods Phys. Special Issue: XXV International Fall Workshop on Geometry and Physics (2017).                                                                                                                                                                            https://arxiv.org/abs/1704.06458
  • A Hamilton–Jacobi theory for implicit differential systems,                                                                                                         O. Esen, M. de León, C. Sardón                                                                                                                                                  Sent to Israel Journal of Mathematics (2017)

 

 

BOOKS 

  • An introduction to Lie systems
    J. de Lucas, C. Sardón
    Accepted in World Scientific 2018
    arXiv:1508.00726

 

PROCEEDINGS

  • Miura reciprocal transformations for two integrable hierarchies in 1+1 dimensions,                                                              P.G. Estévez, C. Sardón,                                                                                                                                             Proceedings GADEIS, Protaras, Cyprus (2012),                                                                                                 https://arxiv.org/abs/1301.3636
  • Quasi-algorithmical construction of reciprocal transformation.                                                                                                  C. Sardón,                                                                                                                                                                   Proceedings   https://arxiv.org/abs/1604.01941
  • Jacobi–Lie systems: fundamentals and low-dimensional classification.                                                                                   F.J. Herranz, J. de Lucas, C. Sardón,                                                                                                                          Proceedings AIMS,  Madrid, Spain (2014).                                                                                                           https://arxiv.org/abs/1412.0300

 

ONGOING WORK

“Quantum Quasi Lie Schemes: properties and applications“,  J.F. Cariñena, J. de Lucas, C. Sardón