55 citations · 486 across the 49 of their papers we have counts for
7 papers · 1 filter
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…