Baecklund Transformations and Rigid Heat Conduction with Memory

B¨acklund Transformations are considered referring to partial differential equations, in general. Then, two different models of a rigid linear heat conductor, with and without memory, are considered. Specifically, the Cole-Hopf transformation which relates the linear heat equation to the nonlinear Burgers equation is assumed as a key notion. Then, a generalization is introduced. In particular, a integro-differential type evolution equation which models heat conduction in a material with memory is shown to be related to a nonlinear hyperbolic equation which can be regarded as a hyperbolic generalization of Burgers equation. Notably, the latter admits wave solutions. An overview on application of Baecklund Transformations is provided referring to heat conduction problems.