Computing Time-periodic Solutions of Nonlinear Systems of Partial Differential Equations*

摘要

We describe an efficient numerical method for the computation of time-periodic solutions of nonlinear systems of partial differential equations. The strategy is to minimize a functional that measures how far solutions of the initial value problem are from being time-periodic by solving an adjoint problem to compute the gradient of the functional. We discuss applications to two different problems in interfacial fluid dynamics, the Benjamin-Ono equation and the vortex sheet with surface tension.