Abstract
In this work, the $$(2+1)$$ -dimensional extended Kadomtsev–Petviashvili equation, which models the surface waves and internal waves in straits or channels, is investigated via the Hirota bilinear method. N-soliton and high-order breather solutions are obtained analytically. Furthermore, mixed solutions consisting of first-order breathers and solitons are also derived, and the corresponding dynamic behaviors are shown by three-dimensional plots. Additionally, based on the long-wave limit, we obtain line rogue waves, lumps and semi-rational solutions composed of lumps, line rogue waves and solitons. It is noteworthy that the semi-rational solutions derived in this paper exhibit elastic interactions.
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