The Kadomtsev-Petviashvili equation is a universal model for the evolution of surface waves of small amplitude propagating in one direction and with weak variations in the transverse direction. The pure initial-value problem was and is extensively studied. This paper deals with the initial-and-boundary-value problem for this equation on a strip with a Dirichlet left boundary condition and two kinds of conditions on the right boundary. Moreover, we treat the case of the half plane and we show a result of convergence.
"An initial and boundary-value problem for the KP-II equation on a strip and on the half plane." Differential Integral Equations 18 (7) 813 - 839, 2005.