Comments on some transformations of systems of Chaplygintype equations
Abstract
Transformations which preserve the structure of systems of Chaplygintype partial differential equations are considered. Rules are formulated for transition from one Chaplygintype system to another which are a generalization of the well known transformation rule of Peres (1944). Formulas for a transformation inverse with respect to the generalized Peres transformation are obtained. The generalized transformations were obtained from the comparison of two equivalent systems of equations describing the steady potential twodimensional flow of a gas in the variables of hodograph velocity space, and also from the comparison of two equivalent linear systems of equations for the unsteady onedimensional flow of a gas with plane waves.
 Publication:

Differentsialnye Uravneniia
 Pub Date:
 January 1976
 Bibcode:
 1976DnU....12...32D
 Keywords:

 Chaplygin Equation;
 Flow Equations;
 Partial Differential Equations;
 Transformations (Mathematics);
 One Dimensional Flow;
 Steady Flow;
 Two Dimensional Flow;
 Unsteady Flow;
 Fluid Mechanics and Heat Transfer