Bäcklund transformations, consistent Riccati expansion solvability, and soliton–cnoidal interaction wave solutions of Kadomtsev–Petviashvili equation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11775047, 11775146 and 11865013) and the Science and TechnologyProject Foundation of Zhongshan City, China (Grant No. 2017B1016).

Abstract

The famous Kadomtsev–Petviashvili (KP) equation is a classical equation in soliton theory. A Bäcklund transformation between the KP equation and the Schwarzian KP equation is demonstrated by means of the truncated Painlevé expansion in this paper. One-parameter group transformations and one-parameter subgroup-invariant solutions for the extended KP equation are obtained. The consistent Riccati expansion (CRE) solvability of the KP equation is proved. Some interaction structures between soliton–cnoidal waves are obtained by CRE and several evolution graphs and density graphs are plotted.