On non-local variational problems with lack of compactness related to non-linear optics

Abstract

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. 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.

30 pages

References in corpus (2)

• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Oscillating tails of dispersion-managed soliton

Cited by in corpus (4)

• On dispersion managed nonlinear Schrödinger equations with lumped amplification
• Quantum Systems at the Brink: Existence of Bound States, Critical Potentials and Dimensionality
• Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities
• Quantum Systems at The Brink