SIMILARITY TRANSFORMATIONS FOR PARTIAL-DIFFERENTIAL EQUATIONS

The importance of similarity transformations and their applications to partial differential equations is discussed. The theory has been pres ented in a simple manner so that it would be beneficial at the undergr aduate level. Special group transformations useful for producing simil arity solutions are investigated. Scaling, translation, and the spiral group of transformations are applied to well-known problems in mathem atical physics, such as the boundary layer equations, the wave equatio n, and the heat conduction equation. Finally, a new transformation inc luding the mentioned transformations as its special cases is also prop osed.