Drone like dynamics of dromion pairs in the (2+1) AKNS equation

We employ Truncated Painlevé Approach (TPA) to the (2+1) dimensional AKNS equation and construct the solutions in closed form in terms of lower dimensional arbitrary functions of space and time. The highlight of our investigation is that we are able to generate dromions undergoing inelastic and elastic collisions. We observe that the conventional dromions undergo inelastic collision not only exchanging their energy, but also their phase while the dromion pair undergoes elastic collision. In particular, we observe that, we are able to turn ON or OFF the dynamic property of dromion pair by selectively choosing the lower dimensional arbitrary functions with a suitable initial condition. Similar to “drones”, Unmanned Aerial Vehicles (UAVs), dromion pairs can be driven anywhere in the two dimensional plane by selectively giving the initial conditions. In addition to dromions, we have also generated a wide class of localized solutions such as rogue waves and lumps. We observe that while the rogue waves are found to be unstable and stationary, lumps do not interact with other, when they travel in the two dimensional plane.