  We study the interactions of two or more solitary waves 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's 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.
New challenges are identified in connection to this model and its solitary
waves.

Pattern Formation and Solitons