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 Kadomtsev-Petviashvili (rmKP) equation. It is shown that with negative dispersion, the rmKP equation is locally well-posed for data in H s1,s2 (ℝ 2) for and s 2 ≥ 0, and hence globally well-posed in the space L 2. 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. © 2012 American Mathematical Society.