Decomposition solutions and Backlund transformations of the BKP and CKP equations

This manuscript introduces a modified formal variable separation approach, showcasing a systematic and notably straightforward methodology for analyzing the B-type Kadomtsev-Petviashvili equation. Through the application of this approach, we successfully ascertain decomposition solutions, Backlund 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 equation, leading to the derivation of decomposition solutions, Backlund 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, the approach establishes an efficient framework for establishing interrelations between diverse systems.