Determining the full transformation relations in the transformation method

TL;DR

This paper reviews a general framework for deriving transformation relations in physical systems governed by PDEs, highlighting its flexibility and potential applications beyond wave control.

Contribution

It clarifies the main concepts of Hu et al.'s general theory and demonstrates its flexibility through an illustrative example.

Findings

The framework can determine transformation relations for arbitrary PDEs.

It differs from traditional methods by offering greater generality.

An example showcases the method's application and flexibility.

Abstract

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 arbitrary partial differential equation (PDE) in its application scope according to the idea of 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.