Numerical Studies of the KP Line Solitons - Osborne, Michelle; McDowell, Tommy (URJ-UCCS: Undergraduate Research Journal at UCCS, 2016)
The Kadomtsev-Petviashvili (KP) equation describes the motion of shallow water waves on a flat two-dimensional region. It admits a class of solitary wave solutions, called line-soliton solutions, which are localized along distinct lines in the xy-plane. These types of solutions have been studied extensively in recent years. Using a variety of initial conditions, the KP equation is simulated numerically, and the interactions of the evolved solitary wave patterns are studied. The goal is to determine to which of the many exact solutions of the KP equation the initial conditions converge.