Reduction operators and exact solutions of generalized Burgers equations

TL;DR

This paper investigates reduction operators for generalized Burgers equations, establishing a link with potential fast diffusion equations, and uses this connection to construct exact solutions.

Contribution

It introduces a novel connection between generalized Burgers equations and potential fast diffusion equations, enabling new exact solutions.

Findings

Established a link between generalized Burgers and potential fast diffusion equations

Constructed exact solutions for generalized Burgers equations

Demonstrated the utility of reduction operators in solving nonlinear PDEs

Abstract

Reduction operators of generalized Burgers equations are studied. A connection between these equations and potential fast diffusion equations with power nonlinearity -1 via reduction operators is established. Exact solutions of generalized Burgers equations are constructed using this connection and known solutions of the constant-coefficient potential fast diffusion equation.