Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation

In this paper we consider a generalized Kadomtsev-Petviashvili equation in the form (Ut + UxXx + UPUx) = Uyy (x, y) E R2, t > 0. It is shown that the solutions blow up in finite time for the supercritical power of nonlinearity p > 4/3 with p the ratio of an even to an odd integer. Moreover, it is shown that the solitary waves are strongly unstable if 2 < p < 4; that is, the solutions blow up in finite time provided they start near an unstable solitary wave.

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