9. Higher order PDEs as systems of first-order PDEs ...
pordlabs.ucsd.edu › rsalmon › 2039. Higher order PDEs as systems of first-order PDEs. Hyperbolic systems. For PDEs, as for ODEs, we may reduce the order by defining new dependent variables. For example, in the case of the wave equation, (1) θ tt = c 2θ xx, the definitions (2) u ≡θ t and v ≡θ x imply (3) u x =v t, while (10) itself may be written as u t = c 2v x. Thus the second-order equation (1) is