Editing Partial differential equation (section)

===Method of characteristics===
{{main|Method of characteristics}}
The characteristic surface in {{math|1=''n'' = ''2''-}}dimensional space is called a '''characteristic curve'''.{{sfn|Zachmanoglou|Thoe|1986|pp=115–116}} 
In special cases, one can find characteristic curves on which the first-order PDE reduces to an ODE – changing coordinates in the domain to straighten these curves allows separation of variables, and is called the [[method of characteristics]].

More generally, applying the method to first-order PDEs in higher dimensions, one may find characteristic surfaces.