Strong Instability of Solitary-Wave Solutions to a Kadomtsev–Petviashvili Equation in Three Dimensions

This paper is concerned with strong instability of solitary-wave solutions of a generalized Kadomtsev–Petviashvili equation in the three-dimensional case(ut+uxxx+upux)x=uyy+uzz (x, y, z) R3, t 0, with p 1. It is shown that the solution, when it is initially close to an unstable solitary wave, blows up in finite time for the power of nonlinearity p<4/3.