Linear stability and instability of ion-acoustic plasma solitary waves

Abstract

The Euler-Poisson equations for a cold, collisionless plasma support ion-acoustic solitary waves. We prove that these waves are spectrally stable at low amplitude in one space-dimension and present numerical evidence that they destabilize at finite amplitude before they develop singularities.

The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation

“…The existence of supersonic solitary waves for (12) has been proven in [19]. The linear stability of those solitary waves was investigated in [13] and their interactions was studied in [12], in particular in comparison with their approximations in the long wave limit by KdV solitary waves. Though our analysis is mainly concerned with the higher dimensional case d = 2, 3, our results apply as well to the system (12) and to provide an alternative proof to [11] of the justification of the KdV approximation.…”

Bifurcation to Coherent Structures in Nonlocally Coupled Systems

“…It is worth noting that an important tool for this analysis, the Evans function [12,1,23] is not available for the nonlocal equations considered here. On the other hands, an analysis as in [16,17], exploiting Evans function analysis for the leading order expansion combined with a perturbation argument as presented here should yield stability information for the type of solutions constructed here for nonlocal equations. More ambitiously, it would be interesting to construct weak interaction manifolds [6,23,27], for spikes with algebraic tail decay constructed here.…”

Dynamical behavior of traveling wave solutions of ion acoustic plasma equations

“…We have the equations discussed by Li and Sattinger [2] and Haragus and Scheel [1] . In this case, the origin (0, 0) is a saddle point of (3), i.e., φ 1 = 0 and h 1 = −(c 2 + 1).…”

“…The existence, the linear stability, and the instability of the smooth solitary waves of (1) have been studied by Haragus and Scheel [1] and Li and Sattinger [2] . For more information on the physical background of these equations, refer to the above two papers and the references therein.…”

“…Especially, the occurrence of breaking wave solutions has not been studied. Therefore, it is very important to understand the dynamics of the traveling wave solutions determined by (1).…”