26 citations · 92 across the 14 of their papers we have counts for
14 papers
Geometry preserving numerical methods for physical systems with finite-dimensional Lie algebras
L. Blanco, F. Jiménez Alburquerque, J. de Lucas +1
We propose a geometric integrator to numerically approximate the flow of Lie systems. The key is a novel procedure that integrates the Lie system on a Lie group intrinsically assoc…
Geometric numerical methods for Lie systems and their application in optimal control
L. Blanco, F. Jiménez, J. de Lucas +1
A Lie system is a non-autonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, a so-called (nonlinear) sup…
Time-dependent Hamiltonian mechanics on a locally conformal symplectic manifold
Orlando Ragnisco, Cristina Sardon, Marcin Zając
In this paper we aim at presenting a concise but also comprehensive study of time-dependent (tdependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We p…
Plasma in monopole background is not twisted Poisson
Manuel Lainz, Cristina Sardon, Alan Weinstein
For a particle in the magnetic field of a cloud of monopoles, the naturally associated 2-form on phase space is not closed, and so the corresponding bracket operation on functions…
A Hamilton-Jacobi formalism for higher order implicit systems
O. Esen, M. de León, C. Sardón
In this paper, we present a generalization of a Hamilton--Jacobi theory to higher order implicit differential equations. We propose two different backgrounds to deal with higher or…
Reduction of a Hamilton-Jacobi equation for nonholonomic systems
Oğul Esen, Manuel de León, Víctor Manuel Jiménez Morales +1
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generali…
A Hamilton-Jacobi theory for implicit differential systems
O. Esen, M. de León, C. Sardón
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, descr…
Geometry of the discrete Hamilton--Jacobi equation. Applications in optimal control
M. de León, C. Sardón
In this paper, we review the discrete Hamilton--Jacobi theory from a geometric point of view. In the discrete realm, the usual geometric interpretation of the Hamilton--Jacobi theo…
A geometric Hamilton--Jacobi theory for a Nambu--Poisson structure
M. de Leon, C. Sardon
The Hamilton-Jacobi theory is a formulation of Classical Mechanics equivalent to other formulations as Newton's equations, Lagrangian or Hamiltonian Mechanics. It is particulary us…
Quasi-algorithmical construction of reciprocal transformations
C. Sardon
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations…
Jacobi-Lie systems: Fundamentals and low-dimensional classification
F. J. Herranz, J. de Lucas, C. Sardon
A Lie system is a system of differential equations describing the integral curves of a -dependent vector field taking values in a finite-dimensional real Lie algebra of vector f…
Lie-Hamilton systems on the plane: Applications and superposition rules
A. Blasco, F. J. Herranz, J. de Lucas +1
A Lie-Hamilton system is a nonautonomous system of first-order ordinary differential equations describing the integral curves of a -dependent vector field taking values in a fin…
Lie symmetries for Lie systems: applications to systems of ODEs and PDEs
P. G. Estévez, F. J. Herranz, J. de Lucas +1
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a g…
Miura Reciprocal transformation for two integrable hierarchies in 1+1 dimensions
P. G. Estevez, C. Sardon
We here present two different hierarchies of PDEs in 1+1 dimensions whose first and second member are the shallow water wave Camassa-Holm and Qiao equations, correspondingly. These…