Painleve analysis of the two-dimensional Burgers equation

Abstract

A Painleve analysis of the two-dimensional Burgers equation is carried out and used to obtain a restricted Backlund transformation that maps a subclass of the solutions of the 1+2D Burgers equation onto a linear heat-like equation. Alternatively, the Backlund transformation can be expressed as a map onto the derivative of the one-dimensional Burgers equation in appropriate dependent and independent variables. The singularity analysis also yields a further class of solutions obtained by solving a Schwarzian differential equation.