Time filter for leapfrog method with a highly nonlinear coupled system of PDEs

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Does anyone know how to use time filter with a system of equations like

  1. $i\dot{\phi} = \chi$
  2. $i \dot{\chi} = - f(\phi)?$

I looked up higher order Robert Asselin filter but the only example I found was a single linear equation however in the original paper in which it was proposed, it was proposed for a general equation but without any nonlinear example.

Any help would be appreciated.