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 $x\to-\infty$ and study their large time asymptotic behavior. We prove that such solutions eject (for $t\to\infty$) a train of curved asymptotic solitons which move behind the basic wave packet. 
A. Boutet de Monvel, E. Khruslov and V. Kotlyarov