Determining the full transformation relations in the transformation method

The transformation method provides an efficient way to control wave propagation by materials. However, the degree to which this transformation concept can be applied to other physical phenomena remains an open question. Recently, Hu et al. presented a general framework for determining the transformation relations of the physical quantities in an arbitrary partial differential equation (PDE) in its application scope according to the idea of the transformation method. In this paper, we will review the main concepts of this general theory, particularly the difference between this idea and usual methods. The flexibility of this method is shown using an example.