Abstract
Under investigation is a -dimensional B-type Kadomtsev–Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, , increasing when . In addition, dark rogue waves are derived when . Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter , and amplitude of the lump soliton is negatively correlated with when .
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