Transformation of auto-B\"{a}cklund type for hyperbolic generalization of Burgers equation

TL;DR

This paper introduces an auto-Bäcklund transformation for a hyperbolic generalization of the Burgers equation with polynomial source, enabling the generation of kink and bi-kink solutions from stationary solutions.

Contribution

The paper presents a novel auto-Bäcklund transformation for the hyperbolic Burgers equation with polynomial source terms, expanding solution methods for this class of nonlinear PDEs.

Findings

Auto-Bäcklund transformation derived for the hyperbolic Burgers equation.

Generation of kink and bi-kink solutions demonstrated.

Transformation applied to stationary solutions to produce new solutions.

Abstract

We consider the hyperbolic generalization of Burgers equation with polynomial source term. The transformation of auto-B\"{a}cklund type was found. Application of the results is shown in the examples, where the pair of two stationary solutions produces kink and bi-kink solutions.