A periodic breather-wave solution is obtained using homoclinic test approach and Hirota’s bilinear method with a small perturbation parameter $u_0$ for the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space–time structure of the lump solution are investigated and discussed using the extreme value theory.
