A new extended (2+1)-dimensional Kadomtsev–Petviashvili equation with N-solitons, periodic solutions, rogue waves, breathers and lump waves

Abstract

In this work, a new extended integrable (2+1)-dimensional Kadomtsev–Petviashvili equation is proposed and investigated, which models slowly varying perturbation wave in dispersion fluids. First, the WTC-Kruskal algorithm is applied to exploring the corresponding compatibility condition for this equation in Painlevé sense. Then, N-soliton, periodic, breather solution as well as the mixed form composing of breather and soliton(s) have been derived via Hirota bilinear method and symbolic computation. Moreover, we have derived the rational and semi-rational solutions in terms of “long wave” limit. The rational solutions can be classified as first order line rogue waves and lumps, while the semi-rational solutions have the forms: a hybrid of first order line rogue wave and one soliton, a hybrid of second order line rogue wave and one soliton, a hybrid of lump and soliton(s), a hybrid of lump and breather, a hybrid of lump and periodic solution.