Phase space method

In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent differential equations.

The solution then becomes a curve in the phase space, parametrized by time.

The (vector) differential equation is reformulated as a geometrical description of the curve, that is, as a differential equation in terms of the phase space variables only, without the original time parametrization.

Finally, a solution in the phase space is transformed back into the original setting.

It can be applied, for example, to find traveling wave solutions of reaction–diffusion systems.