Related papers: Integrable hydrodynamic chains for WZNW model
Exact expressions are derived for the pair and three-body hydrodynamic interactions between a sphere and a number of small particles immersed in a viscous incompressible fluid. The analysis is based on the Stokes equations of low Reynolds…
Operator quantization of the WZNW theory invariant with respect to an affine Kac-Moody algebra $\hat g$ with constrained $\hat {u}(1)^d$ currents is performed using Dirac's procedure. Upon quantization the initial energy-momentum tensor is…
It has been shown by Son and Sur\'owka that the presence of anomaly in hydrodynamics with global U(1) symmetry can induce vortical and magnetic currents. The induced current is uniquely determined by anomaly from the existence of an entropy…
Recent theoretical developments in hydrodynamics of particles with spin 1/2 are briefly reviewed.
The hydrodynamics equations of binary mixtures of Bose gases, Fermi gases, and mixtures of Bose and Fermi gases in the presence of external potentials are derived. These equations can be applied to current experiments on mixtures of atomic…
We classify integrable third order equations in 2+1 dimensions which generalize the examples of Kadomtsev-Petviashvili, Veselov-Novikov and Harry Dym equations. Our approach is based on the observation that dispersionless limits of…
The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation,…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
The lecture notes cover the emergence of generalized hydrodynamics for the classical and quantum Toda chain, the classical Calogero fluid, the Ablowitz-Ladik discretization of the non-linear Schroedinger equation, and the Lieb-Liniger…
A newly proposed framework of perfect-fluid relativistic hydrodynamics for particles with spin 1/2 is briefly reviewed. The hydrodynamic equations follow entirely from the conservation laws for energy, momentum, and angular momentum. The…
Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. Therefore, stable and accurate numerical methods…
We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our constructions…
This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). Integrability corresponds to the…
Hydrodynamic reformulations of the Schr\"odinger equation suggest an interpretation of quantum mechanics in terms of a fluid flowing on configuration space. In the discrete hydrodynamic view, this fluid is not fundamental but emerges from…
Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…
Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time…
In this paper, we have obtained motion equations for a wide class of one-dimensional singularities in 2-D ideal hydrodynamics. The simplest of them, are well known as point vortices. More complicated singularities correspond to vorticity…
In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied.…
The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs…
We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with…