AN INTEGRABLE 4TH-ORDER NONLINEAR EVOLUTION EQUATION APPLIED TO THERMAL GROOVING OF METAL-SURFACES

The fourth-order nonlinear partial differential equation for surface d iffusion is approximated by a new integrable nonlinear evolution equat ion. Exact solutions are obtained for thermal grooving, subject to bou ndary conditions representing a section of a grain boundary. When the slope m of the groove centre is large, the linear model grossly overes timates the groove depth. In the linear model dimensionless groove dep th increases linearly with m, but in the nonlinear model it approaches an upper limit. A nontrivial similarity solution is found for the lim iting case of a thermal groove whose central slope is vertical.