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We show that we can apply the Hirota direct method to some non-integrable equations. For this purpose, we consider the extended Kadomtsev-Petviashvili- Boussinesq (eKPBo) equation with M variable which is (uxxx-6uu x)x + a11uxx + 2ΣMk=2 a1kuxk + ΣMi,j=2aijuxixj=0, where aij = a ji are constants and xi = (x, t, y, z,⋯,x M). We will give the results for M = 3 and a detailed work on this equation for M = 4. Then we will generalize the results for any integer M > 4. © 2009 The Author(s)

Solutions of the Extended Kadomtsev–Petviashvili–Boussinesq Equation by the Hirota Direct Method