Dirk Hundertmark, Young-Ran Lee ON NON-LOCAL VARIATIONAL PROBLEMS WITH LACK OF COMPACTNESS RELATED TO NON-LINEAR OPTICS (388K, pdf) ABSTRACT. We give a simple proof of existence of solutions of the dispersion manage- ment and di raction management equations for zero average dispersion, respectively di raction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.