Soliton asymptotics of rear part of non-localized solutions of the Kadomtsev-Petviashvili equation

We construct non-localized, real global solutions of the Kadomtsev-Petviashvili-I equation which vanish for $x\to -\mathrm{\infty }$ and study their large time asymptotic behavior. We prove that such solutions eject (for $t\to \mathrm{\infty }$) a train of curved asymptotic solitons which move behind the basic wave packet.