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Strong instability of solitary-wave solutions to a Kadomtsev-Petviashvili equation in three dimensions

Abstract This paper is concerned with strong instability of solitary-wave solutions of a generalized Kadomtsev–Petviashvili equation in the three-dimensional case (u t +u xxx +u p u x ) x =u yy +u zz (x, y, z)∈R 3 , 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