Decompositions of the Kadomtsev–Petviashvili equation and their symmetry reductions

Abstract

Starting with a decomposition conjecture, we carefully explain the basic decompositions for the Kadomtsev–Petviashvili (KP) equation as well as the necessary calculation procedures, and it is shown that the KP equation allows the Burgers–STO (BSTO) decomposition, two types of reducible coupled BSTO decompositions and the BSTO–KdV decomposition. Furthermore, we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions. Using the framework of standard Lie point symmetry theory, these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.