Degeneration of breathers in the Kadomttsev-Petviashvili I equation

In this paper, we obtain the high-order breathers of the Kadomttsev-Petviashvili I equation by the Hirota bilinear method and the complexication method. The period, extremum, trajectory and the degeneration of high-order breathers to 1-order breathers are analysed. It's worth noting that we study the full degeneration process of the high-order breathers to high-order lumps by the long wave limit, which means one peak of breather is a very good approximation of lump. In addition, we study the partial degeneration process of high-order breathers which generates the hybrid solutions consisting of soliton, breather, or lump. (C) 2019 Elsevier B.V. All rights reserved.