A method, called beatification, is presented for rapidly extracting weakly nonlinear Hamiltonian systems that describe the dynamics near equilibria of systems possessing Hamiltonian form in terms of noncanonical Poisson brackets. The procedure applies to systems like fluids and plasmas in terms of Eulerian variables that have such noncanonical Poisson brackets, i.e., brackets with nonstandard a...

We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac’s procedure for incorporating constraints. First, the Poisson bracket of moments of the u...

The SBV regularity of weak entropy solutions to the Burgers-Poisson equation for initial data in L 1 ( R ) is considered. We show that derivative a solution consists only absolutely continuous part and jump part.

In the PIC/ MC simulation of materials processing plasmas, (1) one has to solve the Poisson equation in each electron timestep that is very small. Usually this is the rate determining process of numerical simulation. The Poisson equation has been solved using its finite difference form. Since there exists always a thin sheath near a solid boundary, a very fine mesh should be introduced in the s...

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L(R). Additional an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

The theory of the last multipliers as solutions of the Liouville’s transport equation, previously developed for vector fields, is extended here to general multivectors. Characterizations in terms of Witten and Marsden differentials are reobtained as well as the algebraic structure of the set of multivectors with a common last multiplier, namely Gerstenhaber algebra. Applications to Poisson bive...