79 citations · 638 across the 61 of their papers we have counts for
62 papers
Generalized Marsden-Weinstein symplectic structures
Boris Khesin, Klas Modin, Cornelia Vizman
We define a symplectic structure on singular 1-form densities and a presymplectic structure on augmented triples, a compressible analog of the Marsden--Weinstein symplectic structu…
Backward error analysis for matrix discretizations of 2-D Euler equations
Eugen Bronasco, Klas Modin
We introduce a formalism of Lie--Poisson reduction of Butcher series. The corresponding forest momentum map allows for describing backward error analysis of isospectral symplectic…
Madelung hydrodynamics and Poisson geometry of wave functions
Boris Khesin, Klas Modin
We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. We prove that for arbitrary oriented manifolds th…
Arnold stability and rigidity in Zeitlin's model of hydrodynamics
Luca Melzi, Klas Modin
Zeitlin's model is a discretisation of the 2-D Euler equations that preserves the underlying geometric structure. This feature makes it suitable for studying the qualitative behavi…
Universal vector and matrix optimal transport
Boris Khesin, Klas Modin
In this paper we propose a gauge-theoretic approach to the problems of optimal mass transport for vector and matrix densities. This resolves both the issues of positivity and actio…
Symplectic Isospectral Runge--Kutta Methods as Lie group methods
Paolo Cifani, Klas Modin, Cecilia Pagliantini +1
We compare three approaches for structure preserving numerical integration of isospectral flows on quadratic Lie algebras. Such flows originate from Hamiltonian dynamics on the cot…