Decomposition solutions and B\"acklund transformations of the BKP and CKP equations

TL;DR

This paper introduces a modified variable separation approach to derive decomposition solutions, Bäcklund transformations, and Lax pairs for BKP and CKP equations, revealing insights into their integrable structures.

Contribution

It presents a novel, simplified method for obtaining key integrable features of BKP and CKP equations, enhancing understanding of their nonlinear behavior.

Findings

Derived decomposition solutions for BKP and CKP equations

Established Bäcklund transformations and Lax pairs using the new approach

Showed the method's effectiveness in describing integrable systems

Abstract

In this paper, we define the modified formal variable separation approach and show how it determines, in a remarkably simple manner, the decomposition solutions, the B\"acklund transformations, the Lax pair, and the linear superposition solution of the B-type Kadomtsev-Petviashvili equation. Also, the decomposition solutions, the B\"acklund transformation and the Lax pair relating to the C-type Kadomtsev-Petviashvili equation is obtain by the same technique. This indicates that the decomposition may provide a description of integrable behavior in nonlinear systems, while, at the same time, establishing an efficient method for determining relationships between the particular systems.