Related papers: Symmetries of Conservation Laws
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\sc S. Chu, A. Kurganov, and I. Menshov}, Appl. Numer. Math.,…
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…
The main focus of this thesis is the theoretical study of strongly interacting quantum mixtures confined in one dimension and subjected to a harmonic external potential. Such strongly correlated systems can be realized and tested in…
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…
We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a vacuum-compatible family of time-discrete particle…
In this article we find explicit formulae for spherically symmetric solutions of the multidimensional zero-pressure gas dynamics system and its adhesion approximation. The asymptotic behaviour of the explicit solutions of the adhesion…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
We consider the hydrodynamics of relativistic conformal field theories at finite temperature and its slow motions limit, where it reduces to the incompressible Navier-Stokes equations. The symmetries of the equations and their solutions are…
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…
We consider a hydrodynamic-type system of balance equations which is closed by the dynamic equation of state taking into account the effects of spatial nonlocality. Symmetry and local conservation laws of this system are studied. A system…
We study the hydrodynamic-type system of differential equations modeling isothermal no-slip drift flux. Using the facts that the system is partially coupled and its subsystem reduces to the (1+1)-dimensional Klein--Gordon equation, we…
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular measure in initial data. Different approximations can lead to solutions with different…
Gauge invariant conservation laws for the linear and angular momenta are studied in a certain 2+1 dimensional first order dynamical model of vortices in superconductivity. In analogy with fluid vortices it is possible to express the linear…
Basic features of the conservation laws in the Hamiltonian approach to the Poincar\'e gauge theory are presented. It is shown that the Hamiltonian is given as a linear combination of ten first class constraints. The Poisson bracket algebra…
We carry out an extended symmetry analysis of the multi-layer quasi-geostrophic problem. This model is given by a system of an arbitrary number of coupled barotropic vorticity equations. Conservation laws and a Hamiltonian structure for the…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
This article deals with the error estimates for numerical approximations of the entropy solutions of coupled systems of nonlocal hyperbolic conservation laws. The systems can be strongly coupled through the nonlocal coefficient present in…