55 citations · 486 across the 49 of their papers we have counts for
50 papers
A Guide to Applications of -Contact Geometry in Dissipative Field Equations
J. de Lucas, J. Lange, M. Krych
We study the practical scope of the -contact Hamilton--De Donder--Weyl formalism as a geometric framework for dissipative field equations. In particular, our work focuses on can…
Mixed superposition rules for Lie systems, compatible geometric structures, and applications
Rutwig Campoamor-Stursberg, Oscar Carballal, Francisco J. Herranz +1
Mixed superposition rules are, in short, a method to describe the general solutions of a time-dependent system of first-order differential equations, a so-called Lie system, in ter…
A symplectic approach to Schrödinger equations in the infinite-dimensional unbounded setting
Javier de Lucas, Julia Lange, Xavier Rivas
By using the theory of analytic vectors and manifolds modelled on normed spaces, we provide a rigorous symplectic differential geometric approach to -dependent Schrödinger equat…
Quasi-rectifiable Lie algebras for partial differential equations
A. M. Grundland, J. de Lucas
We introduce families of quasi-rectifiable vector fields and study their geometric and algebraic aspects. Then, we analyse their applications to systems of partial differential equ…
An energy-momentum method for ordinary differential equations with an underlying -polysymplectic manifold
Leonardo Colombo, Javier de Lucas, Xavier Rivas +1
This work presents a comprehensive review of the -polysymplectic Marsden-Weinstein reduction theory, rectifying prior errors and inaccuracies in the literature while introducing…
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…
Hamiltonian stochastic Lie systems and applications
E. Fernández-Saiz, J. de Lucas, X. Rivas +1
This paper provides a practical approach to stochastic Lie systems, i.e. stochastic differential equations whose general solutions can be written as a function depending only on a…
On k-polycosymplectic Marsden-Weinstein reductions
J. de Lucas, X. Rivas, S. Vilariño +1
We review and slightly improve the known k-polysymplectic Marsden--Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing…
Cosymplectic geometry, reductions, and energy-momentum methods with applications
J. de Lucas, A. Maskalaniec, B. M. Zawora
Classical energy-momentum methods study the existence and stability properties of solutions of -dependent Hamilton equations on symplectic manifolds whose evolution is given by…
More on superintegrable models on spaces of constant curvature
Cezary Gonera, Joanna Gonera, Javier de Lucas +2
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of the…
Contact Lie systems
Javier de Lucas, Xavier Rivas
We define and analyse the properties of contact Lie systems, namely systems of first-order differential equations describing the integral curves of a -dependent vector field tak…
Quantum quasi-Lie systems: properties and applications
J. F. Cariñena, J. de Lucas, C. Sardón
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a -dependent vector field taking values in a finite-dimensional Lie…
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…
Multiple Riemann wave solutions of the general form of quasilinear hyperbolic systems
A. M. Grundland, J. de Lucas
The objective of this paper is to construct geometrically Riemann -wave solutions of the general form of first-order quasilinear hyperbolic systems of partial differential equat…
Darboux families and the classification of real four-dimensional indecomposable coboundary Lie bialgebras
J. de Lucas, D. Wysocki
This work introduces a new concept, the so-called Darboux family, which is employed to determine, to analyse geometrically, and to classify up to Lie algebra automorphisms, in a re…
A time-dependent energy-momentum method
J. de Lucas, B. M. Zawora
We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisati…
Stratified Lie systems: Theory and applications
J. F. Cariñena, J. de Lucas, D. Wysocki
A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold described by a -dependent vector field ,…
Remarks on superdifferential equations
Janusz Grabowski, Javier de Lucas
We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is just…
Quasi-Lie schemes for PDEs
Jose F. Carinena, Janusz Grabowski, Javier de Lucas
The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of p…
A cohomological approach to immersed submanifolds via integrable systems
A. Michel Grundland, Javier de Lucas
A geometric approach to immersion formulas for soliton surfaces is provided through new cohomologies on spaces of special types of -valued differential forms. This le…
A Grassmann and graded approach to coboundary Lie bialgebras, their classification, and Yang-Baxter equations
J. de Lucas, D. Wysocki
This work pioneers the systematic study and classification (up to Lie algebra automorphisms) of finite-dimensional coboundary Lie bialgebras through Grassmann algebras. Several mat…
Geometric features of Vessiot--Guldberg Lie algebras of conformal and Killing vector fields on
M. M. Lewandowski, J. de Lucas
This paper locally classifies finite-dimensional Lie algebras of conformal and Killing vector fields on relative to an arbitrary pseudo-Riemannian metric. Several re…
Lie-Hamilton systems on curved spaces: A geometrical approach
Francisco J. Herranz, Javier de Lucas, Mariusz Tobolski
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…
A Lie systems approach to the Riccati hierarchy and partial differential equations
J. de Lucas, A. M. Grundland
It is proved that the members of the Riccati hierarchy, the so-called Riccati chain equations, can be considered as particular cases of projective Riccati equations, which greatly…