41 citations · 155 across the 18 of their papers we have counts for
19 papers
Duality of Hamiltonian and Lagrangian formulations for integrable systems
Pierandrea Vergallo, Mats Vermeeren
We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switchin…
Lagrangian multiforms and dispersionless integrable systems
Evgeny V. Ferapontov, Mats Vermeeren
We demonstrate that interesting examples of Lagrangian multiforms appear naturally in the theory of multidimensional dispersionless integrable systems as (a) higher-order conservat…
Discrete Lagrangian Multiforms for ABS Equations I: Quad Equations
Jacob J. Richardson, Mats Vermeeren
Discrete Lagrangian multiform theory is a variational perspective on lattice equations that are integrable in the sense of multidimensional consistency. The Lagrangian multiforms f…
Discrete Lagrangian Multiforms for ABS Equations II: Tetrahedron and Octahedron Equations
Jacob J. Richardson, Mats Vermeeren
We present four types of discrete Lagrangian 2-form associated to the integrable quad equations of the ABS list. These include the triangle Lagrangian that has traditionally been u…
Semi-discrete Lagrangian 2-forms and the Toda hierarchy
Duncan Sleigh, Mats Vermeeren
We present a variational theory of integrable differential-difference equations (semi-discrete integrable systems). This is a natural extension of the ideas known by the names "Lag…
Lagrangian multiforms on Lie groups and non-commuting flows
Vincent Caudrelier, Frank Nijhoff, Duncan Sleigh +1
We describe a variational framework for non-commuting flows, extending the theories of Lagrangian multiforms and pluri-Lagrangian systems, which have gained prominence in recent ye…
Superconvergence of Galerkin variational integrators
Sina Ober-Blöbaum, Mats Vermeeren
We study the order of convergence of Galerkin variational integrators for ordinary differential equations. Galerkin variational integrators approximate a variational (Lagrangian) p…
Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics
Luis C. García-Naranjo, Mats Vermeeren
We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization…
Hamiltonian structures for integrable hierarchies of Lagrangian PDEs
Mats Vermeeren
Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this…
Numerical integration in celestial mechanics: a case for contact geometry
Alessandro Bravetti, Marcello Seri, Mats Vermeeren +1
Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, th…
Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs
Matteo Petrera, Mats Vermeeren
We investigate the relation between pluri-Lagrangian hierarchies of -dimensional partial differential equations and their variational symmetries. The aim is to generalize to the…
Contact variational integrators
Mats Vermeeren, Alessandro Bravetti, Marcello Seri
We present geometric numerical integrators for contact flows that stem from a discretization of Herglotz' variational principle. First we show that the resulting discrete map is a…
A variational perspective on continuum limits of ABS and lattice GD equations
Mats Vermeeren
A pluri-Lagrangian structure is an attribute of integrability for lattice equations and for hierarchies of differential equations. It combines the notion of multi-dimensional consi…
Modified equations for variational integrators applied to Lagrangians linear in velocities
Mats Vermeeren
Variational integrators applied to degenerate Lagrangians that are linear in the velocities are two-step methods. The system of modified equations for a two-step method consists of…
Continuum limits of pluri-Lagrangian systems
Mats Vermeeren
A pluri-Lagrangian (or Lagrangian multiform) structure is an attribute of integrability that has mainly been studied in the context of multidimensionally consistent lattice equatio…
Numerical precession in variational discretizations of the Kepler problem
Mats Vermeeren
Kepler's first law states that the orbit of a point mass with negative energy in a classical gravitational potential is an ellipse with one of its foci at the gravitational center.…
On the Lagrangian structure of integrable hierarchies
Yuri B. Suris, Mats Vermeeren
We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integ…
Modified equations and the Basel problem
Mats Vermeeren
Discretizations of differential equations are often studied through their modified equation. This is a differential equation, usually obtained as a power series, with solutions tha…
Modified Equations for Variational Integrators
Mats Vermeeren
It is well-known that if a symplectic integrator is applied to a Hamiltonian system, then the modified equation, whose solutions interpolate the numerical solutions, is again Hamil…