# On a class of implicit solutions of the continuity and Euler's equations for 1D systems with long range interactions, II

## Détails

ID Serval

serval:BIB_8DBD39D35BC9

Type

**Article**: article d'un périodique ou d'un magazine.

Collection

Publications

Institution

Titre

On a class of implicit solutions of the continuity and Euler's equations for 1D systems with long range interactions, II

Périodique

Physica D: Nonlinear Phenomena

ISSN

0167-2789

Statut éditorial

Publié

Date de publication

2007

Peer-reviewed

Oui

Volume

226

Numéro

2

Pages

173-180

Langue

anglais

Résumé

Results of theoretical and numerical investigations concerning the space-time evolution in ID of Coulombian and Newtonian systems with densities departing from a uniform and homogeneous background are reported here. In the Coulombian case, the model is called a One Component Plasma. In the Newtonian case, we have the cosmological models of Cold Dark Matter in expanding universes with expansion parameters depending or not upon the cosmological constant. A canonical Hamiltonian formulation is given for studying single-speed solutions of their Coulomb- or Jeans-Vlasov-Poisson descriptions. It is shown that using the Gel' fand mass coordinate the equations of motion are exactly integrable and that the corresponding equations of their characteristics are inhomogeneous, linear and second order ODE's with variable coefficients for the cosmological models. It is furthermore shown that, using correlated initial conditions, Burgers' type of implicit equations for the velocity fields are obtained. Comparison is made between this way to generate exact solutions for the characteristics of the models and that put forward by Zel'dovich. Two examples illustrate the resulting regular and singular mean-field dynamics of the models: a periodic initial excess density for the One Component Plasma and a local departure from homogeneity for the cosmological models.

Mots-clé

Coulombian and cosmological models with background densities, Non-local Hamiltonian field theory, Density-velocity correlation, Generalized Burgers equation and mean-field dynamics

Web of science

Création de la notice

07/07/2014 8:38

Dernière modification de la notice

20/08/2019 14:51