Editing Nonlinear system (section)

===Partial differential equations===
{{main|Nonlinear partial differential equation}}
{{See also|List of nonlinear partial differential equations}}
The most common basic approach to studying nonlinear [[partial differential equation]]s is to change the variables (or otherwise transform the problem) so that the resulting problem is simpler (possibly linear). Sometimes, the equation may be transformed into one or more [[ordinary differential equation]]s, as seen in [[separation of variables]], which is always useful whether or not the resulting ordinary differential equation(s) is solvable.

Another common (though less mathematical) tactic, often exploited in fluid and heat mechanics, is to use [[scale analysis (mathematics)|scale analysis]] to simplify a general, natural equation in a certain specific [[boundary value problem]]. For example, the (very) nonlinear [[Navier-Stokes equations]] can be simplified into one linear partial differential equation in the case of transient, laminar, one dimensional flow in a circular pipe; the scale analysis provides conditions under which the flow is laminar and one dimensional and also yields the simplified equation.

Other methods include examining the [[method of characteristics|characteristics]] and using the methods outlined above for ordinary differential equations.