  We study the interactions of two or more solitons in the Adlam-Allen model
describing the evolution of a (cold) plasma of positive and negative charges,
in the presence of electric and transverse magnetic fields. In order to show
that the interactions feature an exponentially repulsive nature, we elaborate
two distinct approaches: (a) using energetic considerations and the Hamiltonian
structure of the model; (b) using the so-called Manton method. We compare these
findings with results of direct simulations, and identify adjustments necessary
to achieve a quantitative match between them. Additional connections are made,
such as with solitons of the Korteweg--de Vries equation. Future challenges are
also mentioned in connection to this model and its solitary waves.
