Partial differential equations Nonlinear system

the common basic approach studying nonlinear partial differential equations change variables (or otherwise transform problem) resulting problem simpler (possibly linear). sometimes, equation may transformed 1 or more ordinary differential equations, seen in separation of variables, useful whether or not resulting ordinary differential equation(s) solvable.

another common (though less mathematic) tactic, seen in fluid , heat mechanics, use scale analysis simplify general, natural equation in specific boundary value problem. example, (very) nonlinear navier-stokes equations can simplified 1 linear partial differential equation in case of transient, laminar, 1 dimensional flow in circular pipe; scale analysis provides conditions under flow laminar , 1 dimensional , yields simplified equation.

other methods include examining characteristics , using methods outlined above ordinary differential equations.