Vassilis Koukouloyiannis
University of the Aegean, Greece
Abstract: The Adlam-Allen (AA) system of partial differential equations is revisited, which, arguably, is the first model that was introduced to describe solitary waves in the context of propagation of hydrodynamic disturbances in collisionless plasmas. The solitary waves of the model are identified by implementing a dynamical systems
approach. The latter suggests that the model also possesses periodic wave solutions. In addition, the connection of the AA system to the Korteweg–de Vries equation is examined. Finally, the interaction between solitons in this model is studied by using both Hamiltonian arguments as well as direct calculations (Manton’s method).