KdV dynamics in the plasma-sheath transition

KdV dynamics in the plasma-sheath transition

A mathematical model is formulated to catch the dynamics hidden in the plasma-sheath transition layer and the inner sheath layer for planar motion of a plasma. It is shown that the rescaled potential in the plasma-sheath transition layer and inner layer is governed by a perturbed KdV equation, through which some of the complex interactions and couplings among physical mechanisms acting in the p...

Near-linear dynamics in KdV

Near-linear evolution in the Korteweg-de-Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction. Mathematics Subject Classification: 35Q53

Wave dynamics in the extended forced KdV

The extended forced Korteweg-de Vries equation (efKdV) is a mathematical model for simulating the interaction of a shallow layer of fluid with external forcing agents. Herein we consider the dynamics of the efKdV when the forcing is assumed to be small and spatially periodic with a timeperiodic variation of the phase. We show that a good heuristic understanding of the dynamics for a certain cla...

Particle dynamics in the KdV approximation

The KdV equation arises in the framework of the Boussinesq scaling as a model equation for waves at the surface of an inviscid fluid. Encoded in the KdV model are relations that may be used to reconstruct the velocity field in the fluid below a given surface wave. In this paper, velocity fields associated to exact solutions of the KdV equation are found, and particle trajectories are computed n...

Stability of the Plasma-sheath