Reciprocal transformations of the one-dimensional magnetogasdynamics

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 has been no general method of obtaining them. Recently such a method was proposed. The method uses group analysis approach and consists of similar steps as for finding an equivalence group of transformations. The new method provides a systematic tool for finding classes of reciprocal transformations (group of reciprocal transformations). The present paper provides an application of this method to the one-dimensional magnetogasdynamics equations of an ideal perfect gas with infinite electrical conductivity. Equivalence groups, groups of reciprocal transformations are presented in the paper.