A LIST OF HODOGRAPH TRANSFORMATIONS AND EXACTLY LINEARIZABLE SYSTEMS

In this paper different kinds of hodograph transformations are studied . The transformations interchange the roles of a different number of d ependent and independent variables in systems of non-linear first-orde r partial differential equations. It is found that these hodograph tra nsformations can be applied to linearize both genuinely non-linear sys tems and quasi-linear systems with more than two dependent variables a nd two independent variables. It is also found that these hodograph tr ansformations can linearize quasi-linear systems which are non-homogen eous in the derivatives. The hodograph transformations derived are app lied to linearize equations encountered in soil and fluid mechanics.