A Method for Finding Reciprocal Transformations

Abstract: Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One of the classes of nonlocal equivalence transformations is the class of reciprocal transformations. Despite the long history of applications of such transformations in continuum mechanics, there is no method of obtaining them. Recently such a method was proposed. The method uses group analysis approach and it consists of similar steps as for finding equivalence group of transformations. The new method provides a systematic tool for finding classes of reciprocal transformations (reciprocal equivalence group of transformations). Similar to the classical group analysis this approach can be also applied for finding all discrete reciprocal transformations (not only composing a group). For an illustration the method is demonstrated by several models applied in hydrodynamics. The author is very thankful to Professor Colin Rogers for attracting my attention to reciprocal transformations.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods