152 research outputs found
Open problems, questions, and challenges in finite-dimensional integrable systems
The paper surveys open problems and questions related to different aspects
of integrable systems with finitely many degrees of freedom. Many of the open
problems were suggested by the participants of the conference “Finite-dimensional
Integrable Systems, FDIS 2017” held at CRM, Barcelona in July 2017.Postprint (updated version
Multi-symplectic discretisation of wave map equations
We present a new multi-symplectic formulation of constrained Hamiltonian
partial differential equations, and we study the associated local conservation
laws. A multi-symplectic discretisation based on this new formulation is
exemplified by means of the Euler box scheme. When applied to the wave map
equation, this numerical scheme is explicit, preserves the constraint and can
be seen as a generalisation of the Shake algorithm for constrained mechanical
systems. Furthermore, numerical experiments show excellent conservation
properties of the numerical solutions
Open problems, questions, and challenges in finite-dimensional integrable systems
The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference ‘Finite-dimensional Integrable Systems, FDIS 2017’ held at CRM, Barcelona in July 2017.Peer ReviewedPostprint (author's final draft
Absolute points of correlations of
The sets of the absolute points of (possibly degenerate) polarities of a projective space
are well known. The sets of the absolute points of (possibly degenerate) correlations,
different from polarities, of PG(2, qn), have been completely determined by B.C.
Kestenband in 11 papers from 1990 to 2014, for non-degenerate correlations and
by D’haeseleer and Durante (Electron J Combin 27(2):2–32, 2020) for degenerate
correlations. In this paper, we completely determine the sets of the absolute points
of degenerate correlations, different from degenerate polarities, of a projective space
PG(3, qn). As an application we show that, for q even, some of these sets are related
to the Segre’s (2h +1)-arc of PG(3, 2n) and to the Lüneburg spread of PG(3, 22h+1)
Open problems, questions, and challenges in finite-dimensional integrable systems
The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference “Finite-dimensional Integrable Systems, FDIS 2017” held at CRM, Barcelona in July 2017
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