Local regularity and decay estimates of solitary waves for the rotation-modified Kadomtsev-Petviashvili equation

Abstract

This paper is mainly concerned with the local low regularity of solutions and decay estimates of solitary waves to the rotation-modified KadomtsevPetviashvili (rmKP) equation. It is shown that with negative dispersion, the rmKP equation is locally well-posed for data in Hs1,s2 (R2) for s1 > − 13 and s2 > 0, and hence globally well-posed in the space L2. Moreover, an improved result on the decay property of the solitary waves is established, which shows that all solitary waves of the rmKP equation decay exponentially at infinity.