Magnetic skyrmions have attracted enormous research interest since their discovery a
decade ago. The non-trivial real-space topology of these nano-whirls leads to fundamentally …

The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of
degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom …

The stability of solitons is reviewed for nonlinear conservative media. The main attention is
paid to the description of the methods: perturbation theory, inverse scattering transform …

This paper is a study of incompressible fluids, especially their Clebsch variables and
vortices, using symplectic geometry and the Lie-Poisson structure on the dual of a Lie …

The Hamiltonian description of hydrodynamic type systems in application to plasmas,
hydrodynamics, and magnetohydrodynamics is reviewed with emphasis on the problem of …

Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant,
attract an intense attention in the diverse areas of physics ranging from high-energy physics …

Maxwell equations in vacuum allow for solutions with a non-trivial topology in the electric
and magnetic field line configurations at any given moment in time. One example is a space …

We are investigating the inviscid limit of the Navier–Stokes equation, and we find previously
unknown anomalous terms in Hamiltonian, Dissipation, and Helicity, which survive this limit …

We propose a novel Clebsch method to simulate the free-surface vortical flow. At the center
of our approach lies a level-set method enhanced by a wave-function correction scheme …

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be
steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non …