Related papers: Hydrodynamic chains and a classification of their …
Integrable deformations of a class of Rikitake dynamical systems are constructed by deforming their underlying Lie-Poisson Hamiltonian structures, which are considered linearizations of Poisson--Lie structures on certain (dual) Lie groups.…
Some applications of the odd Poisson bracket developed by Kharkov's theorists are represented, including the reformulation of classical Hamiltonian dynamics, the description of hydrodynamics as a Hamilton system by means of the odd bracket…
Kinetic theory describes a dilute monatomic gas using a distribution function $f(q,p,t)$, the expected phase-space density of particles. The distribution function evolves according to the collisionless Boltzmann equation in the high Knudsen…
Integrability condition of Hamiltonian perturbations of integrable Hamiltonian PDEs of hydrodynamic type up to the second order approximation is considered.
This paper investigates Hamiltonian properties of the algebro-geometric discretization of KP hierarchy introduced in \cite{Gie1}. A Poisson bracket is introduced. The system is related to the periodic band matrix system of \cite{vM-M}. It…
A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…
We develop a Lie group geometric framework for the motion of fluids with permeable boundaries that extends Arnold's geometric description of fluid in closed domains. Our setting is based on the classical Hamilton principle applied to fluid…
The complete integrability of a generalized Riemann type hydrodynamic system is studied by means of symplectic and differential-algebraic tools. A compatible pair of polynomial Poissonian structures, Lax type representation and related…
The integrability of an m-component system of hydrodynamic type, u_t=V(u)u_x, by the generalized hodograph method requires the diagonalizability of the mxm matrix V(u). This condition is known to be equivalent to the vanishing of the…
This article analyzes the formulation of space-time continuous hyperbolic hydrodynamic models for systems of interacting particles moving on a lattice, by connecting their local stochastic lattice dynamics to the formulation of an…
We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial $C_{\infty v}$-symmetry to biaxial systems exhibiting local $C_{2v}$-symmetry. Our work is motivated by the recently…
We introduce the cluster algebraic formulation of the integrable difference equations, the discrete Lotka-Volterra equation and the discrete Liouville equation, from the view point of the general T-system and Y-system. We also study the…
We review a (constructive) approach first introduced in [6] and further developed in [7, 8, 38, 9] for hydrodynamic limits of asymmetric attractive particle systems, in a weak or in a strong (that is, almost sure) sense, in an homogeneous…
Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain "Bethe-Boltzmann" kinetic equation, which has the form of an…
We study Poisson structures of dynamical systems with three degrees of freedom which are known for their chaotic properties, namely L\"u, modified L\"u, Chen, $T$ and Qi systems. We show that all these flows admit bi-Hamiltonian structures…
The theory of differential forms began with a discovery of Poincare who found conservation laws of a new type for Hamiltonian systems - The Integral Invariants. Even in the absence of non-trivial integrals of motion, there exist invariant…
In this two-parts paper, we present a systematic procedure to extend the known Hamiltonian model of ideal inviscid fluid flow on Riemannian manifolds in terms of Lie-Poisson structures to a port-Hamiltonian model in terms of Stokes-Dirac…
We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets…
Some ideas relating to a bracket formulation for dissipative systems are considered. The formulation involves a bracket that is analogous to a generalized Poisson bracket, but possesses a symmetric component. Such a bracket is presented for…
We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is…