Similarity Transformations for Partial Differential Equations

Abstract

The importance of similarity transformations and their applications to partial differential equations is discussed. The theory has been presented in a simple manner so that it would be beneficial at the undergraduate level. Special group transformations useful for producing similarity solutions are investigated. Scaling, translation, and the spiral group of transformations are applied to well-known problems in mathematical physics, such as the boundary layer equations, the wave equation, and the heat conduction equation. Finally, a new transformation including the mentioned transformations as its special cases is also proposed.