Related papers: Symmetry properties of some Euler-type equations i…
We introduce the notion of a partial dynamical symmetry for which a prescribed symmetry is neither exact nor completely broken. We survey the different types of partial dynamical symmetries and present empirical examples in each category.
Exact solutions to the static equilibrium magnetohydrodynamic equations are presented and discussed for both axially and helically reduced systems. For both symmetries, physical restrictions on the solutions are discussed and it is seen…
We provide a complete classification of generalized and formal symmetries and local conservation laws for an evolution equation which generalizes the Kawahara equation having important applications in the study of plasma waves and…
We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…
The group properties of the shallow-water equations with the complete Coriolis force is the subject of this study. In particular we apply the Lie theory to classify the system of three nonlinear partial differential equations according to…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric structures, such as conservation laws, presymplectic…
This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the…
In this paper we prove some symmetry results for entire solutions to the semilinear equation $-\Delta u=f(u)$, with $f$ nonincreasing in a right neighbourhood of the origin. We consider solutions decaying only in some directions and we give…
The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed three-dimensional plasma systems in a way consistent with chaos theory is…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
We consider a linearized Euler--Maxwell model for the propagation and absorption of electromagnetic waves in a magnetized plasma. We present the derivation of the model, and we show its well-posedeness, its strong and polynomial stability…
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
The system of equations of electromagnetic self-consistency in a plasma is analytically solved for the case of a two-component homogeneous plasma in the non-relativistic approximation.
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…
Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The…
We describe kinetic simulations of transient problems in partially ionized weakly-collisional plasma around spherical bodies absorbing or emitting charged particles. Numerical solutions of kinetic equations for electrons and ions in 1D2V…
We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced…
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Three different structure preserving discretizations of the…