相关论文: A Lax Description for Polytropic Gas Dynamics

The two-dimensional shallow water equations in Eulerian and Lagrangain coordinates are considered. Lagrangian and Hamiltonian formalism of the equations is given. The transformations mapping the two-dimensional shallow water equations with…

An alternative method of constructing the formal diagonalization for the discrete Lax operators is proposed which can be used to calculate conservation laws and in some cases generalized symmetries for discrete dynamical systems. Discrete…

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such…

This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably…

In our previous work, a unified description as polynomial Hamiltonian systems was established for a broad class of the Schlesinger systems including the sixth Painleve equation and Garnier systems. The main purpose of this paper is to…

In any generally covariant theory of gravity, we show the relationship between the linearized asymptotically conserved current and its non-linear completion through the identically conserved current. Our formulation for conserved charges is…

The long time behavior of a couple of interacting asymmetric exclusion processes of opposite velocities is investigated in one space dimension. We do not allow two particles at the same site, and a collision effect (exchange) takes place…

We consider 1+1 - dimensional non-homogeneous systems of hydrodynamic type that possess Lax representations with movable singularities. We present a construction, which provides a wide class of examples of such systems with arbitrary number…

Lame equation arises from deriving Laplace equation in ellipsoidal coordinates; in other words, it's called ellipsoidal harmonic equation. Lame function is applicable to diverse areas such as boundary value problems in ellipsoidal geometry,…

We descibe a number of dynamical systems that are generalizations of S. Kowalevskaya system and admit the Lax representation.

The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…

A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…

Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition…

A generalized two-component model with peakon solutions is proposed in this paper. It allows an arbitrary function to be involved in as well as including some existing integrable peakon equations as special reductions. The generalized…

A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being…

The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…

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…

We derive the pressure tensor and the heat flux to accompany the new macroscopic conservation equations that we developed previously in a volume-based kinetic framework for gas flows. This kinetic description allows for expansion or…

We consider equations arising from rational Lax representations. A general method to construct recursion operators for such equations is given. Several examples are given, including a degenerate bi-Hamiltonian system with a recursion…

The particular case of the integrable two component (2+1)-dimensional hydrodynamical type systems, which generalises the so-called Hamiltonian subcase, is considered. The associated system in involution is integrated in a parametric form. A…