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 method consists of rewriting the equations as a first-order system by introducing additional variables. The original and the new variables form a vector in the phase space. The solution to then becomes a curve, called a trajectory, parametrized by time, in the phase space. The solution is found by passing to other descriptions of the curve, without the original time parametrization.
The phase space method is often used to find traveling wave solutions of reaction-diffusion systems.[1][2]
References
- ^ A. Kolmogorov, I. Petrovskii, and N. Piscounov. A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem. In V. M. Tikhomirov, editor, Selected Works of A. N. Kolmogorov I, pages 248--270. Kluwer 1991. Translated by V. M. Volosov from Bull. Moscow Univ., Math. Mech. 1, 1--25, 1937
- ^ Peter Grindrod. The theory and applications of reaction-diffusion equations: Patterns and waves. Oxford Applied Mathematics and Computing Science Series. The Clarendon Press Oxford University Press, New York, second edition, 1996.