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Under investigation is a new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation. The main results are listed as follows: (i) lump solutions; (ii) interaction solutions between lump wave and solitary waves; (iii) interaction solutions between lump wave and periodic waves; and (iv) breather wave solutions. Furthermore, graphical representation of all solutions is studied and shown in some 3D and contour plots.

Breather wave and lump‐type solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid