Decomposition solutions and Bäcklund transformations of the B-type and C-type Kadomtsev–Petviashvili equations

Abstract

This paper introduces a modified formal variable separation approach, showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev–Petviashvili (BKP) equation. Through the application of this approach, we successfully ascertain decomposition solutions, Bäcklund transformations, the Lax pair, and the linear superposition solution associated with the aforementioned equation. Furthermore, we expand the utilization of this technique to the C-type Kadomtsev–Petviashvili (CKP) equation, leading to the derivation of decomposition solutions, Bäcklund transformations, and the Lax pair specific to this equation. The results obtained not only underscore the efficacy of the proposed approach, but also highlight its potential in offering a profound comprehension of integrable behaviors in nonlinear systems. Moreover, this approach demonstrates an efficient framework for establishing interrelations between diverse systems.