Soliton solutions, B\"acklund transformation and Lax pair for coupled Burgers system via Bell polynomials

TL;DR

This paper investigates the integrability of a coupled Burgers system using binary Bell polynomials, deriving bilinear forms, soliton solutions, B"acklund transformations, and a Lax pair to demonstrate its integrable structure.

Contribution

It introduces a novel application of binary Bell polynomials to analyze the integrability of the coupled Burgers system, providing explicit solutions and transformations.

Findings

Derived bilinear form and soliton solutions

Established B"acklund transformations for the system

Obtained Lax pair confirming integrability

Abstract

In this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these solutions are given. We also get B\"acklund transformations in both binary Bell polynomial form and bilinear form. Based on the B\"acklund transformation, Lax pair is obtained. Namely, this is a study in which integrabilitiy of coupled burgers system is investigated.