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

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, B & auml;cklund 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, B & auml;cklund 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.