Abstract
This paper investigates some novel exact analytical solutions, including lump-type wave, breather wave as well as BK-type wave solutions for a (3+1)-dimensional p¯-gKP equation. Firstly, the trilinear p¯-gKP equation is well established by the multivariate trilinear operators. Secondly, three types of wave solutions for the p¯-gKP equation are obtained by utilizing the trilinear method. A kind of new interaction solutions among the breather wave and the kink-type waves are also generated, i.e. the so called BK-type waves, which enriches the types of solutions of PDEs. Through the way of resetting different space constants, we adjust the coordinates of kink-type waves in order for them colliding with the breather wave, after that, the transformed kink-type waves gradually swallow the breather wave. Finally, the solitary wave solutions for the (3+1)-dimensional gKP equation are successfully constructed through using a perturbation method.
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