Computation of Time-Periodic Solutions of the Benjamin-Ono Equation

@article{Ambrose2010ComputationOT,
  title={Computation of Time-Periodic Solutions of the Benjamin-Ono Equation},
  author={David M. Ambrose and Jon Wilkening},
  journal={J. Nonlinear Science},
  year={2010},
  volume={20},
  pages={277-308}
}
We present a spectrally accurate numerical method for finding non-trivial timeperiodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which… CONTINUE READING
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