Abstract
In this paper, the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation is an object of the research. Based on the extended homogeneous balancing method, Auto-Bäcklund transformations are obtained in two cases. Subsequently, with the help of these transformations, we obtain various explicit solutions of this equation. We attain complexiton solutions consisting of exponential, hyperbolic and trigonometric solutions from the Hirota bilinear form of this equation through the extended transformed rational function method. Also, we derive one-kink and two-kink soliton solutions by Maple symbolic calculation and the breather-wave solution via the extended homoclinic test approach. In addition, 3D graphics and density plots of the obtained solutions are depicted to illustrate the dynamical features of these solutions.
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