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In this paper we consider a generalized Kadomtsev-Petviashvili equation in the form 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.doi:10.1090/s0002-9947-00-02465-x fatcat:pnwxmyaxvngxlag7svhswtsdp4