55 citations · 486 across the 49 of their papers we have counts for
36 papers · 1 filter
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…
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…
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…
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…
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…
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…
Lie systems and Schrödinger equations
J. F. Cariñena, J. Clemente-Gallardo, J. A. Jover-Galtier +1
We prove that -dependent Schrödinger equations on finite-dimensional Hilbert spaces determined by -dependent Hermitian Hamiltonian operators can be described through Lie syst…
Geometry of Riccati equations over normed division algebras
J. de Lucas, M. Tobolski, S. Vilariño
This work presents and studies Riccati equations over finite-dimensional normed division algebras. We prove that a Riccati equation over a finite-dimensional normed division algebr…
Jacobi multipliers, non-local symmetries and nonlinear oscillators
J. F. Cariñena, J. de Lucas, M. F. Rañada
Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last mult…
A new application of k-symplectic Lie systems
J. de Lucas, M. Tobolski, S. Vilariño
The -symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the -sy…
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…
k-symplectic Lie systems: theory and applications
J. de Lucas, S. Vilariño
A Lie system is a system of first-order ordinary differential equations describing the integral curves of a -dependent vector field taking values in a finite-dimensional real Li…
Lie-Hamilton systems on the plane: properties, classification and applications
A. Ballesteros, A. Blasco, F. J. Herranz +2
We study Lie-Hamilton systems on the plane, i.e. systems of first-order differential equations describing the integral curves of a -dependent vector field taking values in a fin…
From constants of motion to superposition rules for Lie-Hamilton systems
A. Ballesteros, J. F. Cariñena, F. J. Herranz +2
A Lie system is a nonautonomous system of first-order differential equations possessing a superposition rule, i.e. a map expressing its general solution in terms of a generic finit…