Hodograph Transformations and Hodograph Invariant Differential Equations (original) (raw)

A phenomenon present in many physical problems hodograph invariance of partial differential equations is considered for two-dimensional submanifolds in three-and four-dimensional spaces. This means that the equation keeps its shape when interchanging the roles of any of the functions and arguments, i. e. under a hodograph transformation. For that purpose unified formulations for hodograph transformations are obtained. A method for the formation of hodograph invariant equations is shown. The well-known scalar Born-Infeld equation and its two-component generalization prove