We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.
The Korteweg–de Vries equation which describes cylindrical or spherical converging ion-acoustic waves is solved numerically. Soliton-like structures are shown to be generated not only from compressive but also from rarefactive and mixed initial pulses. The velocity of the soliton-like structures is dependent on the initial pulse shape.
Propagation of nonlinear ion-acoustic waves in a multi-component plasma with negative ions is investigated experimentally. At a critical concentration of negative ions, both compressive and rarefactive solitons are observed. The velocities and widths of the solitons are measured and compared with the soliton solutions of the modified Korteweg–de Vries equation and of the pseudopotential method. The modified Korteweg–de Vries equation is solved numerically to investigate overtaking collisions of a positive and a negative soliton. Fluid equations together with Poisson's equation are numerically integrated to simulate their head-on collisions.
Quasi-soliton solution of Korteweg-de Vries equation and its application in ion acoustic waves
