Blow up and instability of solitary wave solutions to a generalized Kadomtsev-Petviashvili equation and two-dimensional Benjamin-Ono equations

Let p >= 2 with p being the ratio of an even to an odd integer. For the generalized Kadomtsev Petviashvili equation, coupled with Benjamin Ono equations, in the form (u(t) + u(xxx) +beta Hu(xx) +u(p)u(x))(x) = u(yy), (x, y)is an element of R-2, t >= 0, it is proved that the solutions blow up infinite time even for those initial data with positive energy. As a by-product, it is proved that for all c >(beta/2) , the solitary waves phi(x-ct, y); are strongly unstable if 2 <= p < 4. This result, even in a special case beta=0, improves a previous work by Liu ( Liu 2001 Trans. AMS 353, 191 208) where the instability of solitary waves was proved only in the case of 2 < p < 4.