STUDY OF A HODOGRAPH TRANSFORMATION AND ITS APPLICATIONS

摘要

A hodograph transformation found useful in linearizing equations in civil engineering is studied in this paper. The characteristics of the linearizable systems associated with the hodograph transformation are calculated. The general expressions of the linearizable parabolic and hyperbolic systems associated with the hodograph transformation are derived. The link between the hodograph transformation and the reciprocal transformation proposed by Kingston and Rogers is also studied and the merits of the hodograph transformation are pointed out. A new application of the hodograph transformation, namely, the reduction of the order of some nonlinear second order partial differential equations, is also presented. Two new examples are given for the linearization of nonlinear partial differential equation by the hodograph transformation.