Stability of nonlinear ion sound waves and solitons in plasmas

Abstract

Abstract Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the K. –de V. equation, which gives stability for the nonlinear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5. A three-dimensional generalization of the K. –de V. equation is considered but this leads to stability for all nonlinear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit.