A point transformation between forms of the generalised burgers equation

Abstract

This Letter describes a point transformation between forms of one of the fundamental equations of nonlinear acoustics, the generalised Burgers equation (gBE). This transformation gives rise to a number of new results on the gBE, including the identification of two of the three standard forms of gBE, and new exact solutions to the “exponential horn” gBE. It also reduces to a point symmetry of the Burgers equation itself, and relates the Taylor and Khokhlov solutions of the Burgers equation.