Formulation of a Connection for Prolongations and an Application to the Burgers-KdV Equation

The Wahlquist-Estabrook approach which has been applied to investigate the prolongation structure of many nonlinear systems is introduced. The theory which results is applied to the Burgers-KdV equation which is shown to have a nontrivial prolongation algebra. It is shown that the resulting equations can be solved to produce a very general solution. Based on the results determined for the algebra, without picking a specific representation for the algebra, a Lax pair for the equation is determined in terms of the basic generators of the algebra.