Collisions of acoustic solitons and their electric fields in plasmas at critical compositions

Abstract

Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg–de Vries (KdV) equation. In multispecies plasmas at critical compositions the coefficient of the quadratic nonlinearity vanishes. Extending the analytic treatment then leads to a modified KdV (mKdV) equation, which is characterized by a cubic nonlinearity and is even in the electrostatic potential. The mKdV equation admits solitons having opposite electrostatic polarities, in contrast to KdV solitons which can only be of one polarity at a time. A Hirota formalism has been used to derive the two-soliton solution. That solution covers not only the interaction of same-polarity solitons but also the collision of compressive and rarefactive solitons. For the visualization of the solutions, the focus is on the details of the interaction region. A novel and detailed discussion is included of typical electric field signatures that are often observed in ionospheric and magnetospheric plasmas. It is argued that these signatures can be attributed to solitons and their interactions. As such, they have received little attention.