相关论文: On the Complete Integrability of a One Generalized…
We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous…
We study bi-Hamiltonian systems of hydrodynamic type with non-singular (semisimple) non-local bi-Hamiltonian structures and prove that such systems of hydrodynamic type are diagonalizable. Moreover, we prove that for an arbitrary…
Construction of a nonlinear higher-order thermo-hydrodynamics, including correlations, in the framework of a Generalized Nonequilibrium Statistical Grand-Canonical Ensemble is presented. In that way it is provided a particular formalism for…
We solve the problem of reducing to the simplest and convenient for our purposes, canonical form for an arbitrary pair of compatible nonlocal Poisson brackets of hydrodynamic type generated by metrics of constant Riemannian curvature in…
The first example of the so-called "coupled" integrable hydrodynamic chain is presented. Infinitely many commuting flows are derived. Compatibility conditions of the first two of them lead to the remarkable Manakov--Santini system.…
We classify integrable Hamiltonian equations in 3D with the Hamiltonian operator d/dx, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w such that w_x=u_y. Based on the method…
Lagrangian multiform theory is a variational framework for integrable systems. In this article we introduce a new formulation which is based on symplectic geometry and which treats position, momentum and time coordinates of a…
Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The…
We study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties $V_{n,r}$. The systems are integrable in the non-commutative sense, and by applying a $2r\times…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and…
The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential…
We consider the discrete Boussinesq integrable system and the compatible set of differential difference, and partial differential equations. The latter not only encode the complete hierarchy of the Boussisesq equation, but also incorporate…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…
We consider nonholonomic geodesic flows of left-invariant metrics and left-invariant nonintegrable distributions on compact connected Lie groups. The equations of geodesic flows are reduced to the Euler-Poincare-Suslov equations on the…
A port-Hamiltonian model for compressible Newtonian fluid dynamics is presented in entirely coordinate-independent geometric fashion. This is achieved by use of tensor-valued differential forms that allow to describe describe the…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
The detection of gravitational waves has opened a new era for astronomy, allowing for the combined use of gravitational wave and electromagnetic emissions to directly probe the physics of compact objects, still poorly understood. So far,…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
We introduce anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on cosymplectic manifolds. We investigate necessary and…