Abstract
In this paper, a Kadomtsev–Petviashvili–Boussinesq-like equation in (3+1)-dimensions is firstly introduced by using the combination of the Hirota bilinear Kadomtsev–Petviashvili equation and Boussinesq equation in terms of function f. And then a direct bilinear Backlund transformation of this new model is constructed, which consists of seven bilinear equations and ten arbitrary parameters. Based on this constructed bilinear Backlund transformation, some classes of exponential and rational traveling wave solutions with arbitrary wave numbers are presented.
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