相关论文: Integrable hydrodynamic chains

Extensions to kinetic theory and hydrodynamic models are proposed that account for the existence of multi-particle contacts. In the presence of multi-particle contacts (involving elastic, reversible, potential contact energy), dissipation…

The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…

We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same type which is still bihamiltonian.

Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…

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 methods of statistical dynamics are applied to a fluid with 5 conserved fields (the mass, the energy, and the three components of momentum) moving in a given external potential. When the potential is zero, we recover a previously…

The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from…

We obtain the hydrodynamic limit of one-dimensional interacting particle systems describing the macroscopic evolution of the density of mass in infinite volume from the microscopic dynamics. The processes are weak pertubations of the…

We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be…

Quantum integrable systems, such as the interacting Bose gas in one dimension and the XXZ quantum spin chain, have an extensive number of local conserved quantities that endow them with exotic thermalization and transport properties. We…

For a class of Hamiltonian systems naturally arising in the modern theory of separation of variables, we establish their maximal superintegrability by explicitly constructing the additional integrals of motion.

We show that hydrodynamic diffusion is generically present in many-body interacting integrable models. We extend the recently developed generalised hydrodynamic (GHD) to include terms of Navier-Stokes type which lead to positive entropy…

We introduce non-perturbative analytical techniques for the derivation of the hydrodynamic manifolds from kinetic equations. The new approach is analogous to the Schwinger-Dyson equation of quantum field theories, and its derivation is…

Conventional hydrodynamics describes systems with few long-lived excitations. In one dimension, however, many experimentally relevant systems feature a large number of long-lived excitations even at high temperature, because they are…

3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…

Magnetorheological fluids consist of micrometer-sized magnetic particles in a carrier liquid. Sufficiently strong external magnetic fields lead to the formation of string-like particle aggregates. We demonstrate that hydrodynamic…

We construct infinite families of new universality classes of fracton hydrodynamics with momentum conservation, both with multipole conservation laws and/or subsystem symmetry. We explore the effects of broken inversion and/or time-reversal…

It is shown how the dimension of any arbitrary over-determined system of differential equations can be reduced, which makes the system suitable for numerical solution modeling. Specifically, over-determined equations of hydrodynamics are…

This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical…

The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…