LAUSR

Abstract In this paper we study special properties of solutions of the initial value problem (IVP) associated to the fifth order Kadomtsev-Petviashvili II equation. Mainly, for initial data ϕ ∈ H 1 + ( R 2 ) whose restriction belongs to H m ( ( x 0 , ∞ ) × R ) for some m ∈ Z + , m ≥ 2 and x 0 ∈ R , we prove that the restriction of the corresponding solution u ( ⋅ , t ) belongs to H m ( ( b , ∞ ) × R ) for any b ∈ R and any t > 0 . In other words, the extra regularity on the data propagates in the solutions in the direction of the dispersion.