相关论文: Integrable tops and non-commutative torus

We derive the vorticity equation for an incompressible fluid on a 2-dimensional surface with arbitrary topology embedded in 3-dimensional Euclidean space by using a tailored Clebsch parametrization of the flow. In the inviscid limit, we…

It is well known that the Laplace cascade method is an effective tool for constructing solutions to linear equations of hyperbolic type, as well as nonlinear equations of the Liouville type. The connection between the Laplace method and…

We show that Laplace isospectral deformations within a conformal class of generic Liouville metrics on the two-dimensional torus that are linear in the deformation parameter are necessarily trivial. Two of the main ingredients in our proof…

A hybrid system is a system whose dynamics are controlled by a mixture of both continuous and discrete transitions. The integrability of Hamiltonian systems is often identified with complete integrability or Liouville integrability, that…

Arnold showed that the Euler equations of an ideal fluid describe geodesics on the Lie algebra of incompressible vector fields. We generalize this to fluids with dissipation and Gaussian random forcing. The dynamics is determined by the…

We show, that higher analogs of the Willmore functional, defined on the space of immersions M^2\rightarrow R^3, where M^2 is a two-dimensional torus, R^3 is the 3-dimensional Euclidean space are invariant under conformal transformations of…

In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…

We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…

Starting from a microscopic multiparticle Langevin equation, we systematically derive a hydrodynamic description in terms of density and momentum fields for chiral active particles interacting via standard repulsive and nonlocal odd forces.…

We consider the equilibrium equations for a conducting elastic rod placed in a uniform magnetic field, motivated by the problem of electrodynamic space tethers. When expressed in body coordinates the equations are found to sit in a…

We find the hydrodynamic equations of a system of particles constrained to be in the lowest Landau level. We interpret the hydrodynamic theory as a Hamiltonian system with the Poisson brackets between the hydrodynamic variables determined…

Local structures, beyond the well-known `frozen-in' to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler…

In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incompressible Euler equation in two dimensions. The fluids are…

Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually related to the so-called {\it ideal tracer particles}. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as…

For a wide class of linear Hamiltonian operators we develop a general criterion that characterizes the unstable eigenvalues as the zeros of a holomorphic function given by the determinant of a finite-dimensional matrix. We apply the latter…

We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…

A rigidly rotating incompressible perfect fluid solution of Einstein's gravitational equations is discussed. The Petrov type is D, and the metric admits a four-parameter isometry group. The Gaussian curvature of the constant-pressure…

The St\"ackel transform is applied to the geodesic motion on Euclidean space, through the harmonic oscillator and Kepler-Coloumb potentials, in order to obtain maximally superintegrable classical systems on N-dimensional Riemannian spaces…

This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants,…

We consider the interaction of two vortex patches (elliptic Kirchhoff vortices) which move in an unbounded volume of an ideal incompressible fluid. A moment second-order model is used to describe the interaction. The case of integrability…