In this paper different kinds of hodograph transformations are studied. The transformations interchange the roles of a different number of dependent and independent variables in systems of non-linear first-order partial differential equations. It is found that these hodograph transformations can be applied to linearize both genuinely non-linear systems and quasi-linear systems with more than two dependent variables and two independent variables. It is also found that these hodograph transformations can linearize quasi-linear systems which are non-homogeneous in the derivatives. The hodograph transformations derived are applied to linearize equations encountered in soil and fluid mechanics.
- Exactly linearizable systems
- Hodograph transformations