In the first part of my talk, I present the classical dual variational method in the context of Nonlinear Helmholtz equations that describe monochromatic waves in nonlinear materials. Afterwards, I discuss two recent generalizations of the method. The first deals with an extension to Nonlinear Helmholtz equations with sign-changing nonlinearities. For these problems we construct solutions that have infinite Morse-Index in the dual variational formulation. The second generalization concerns dual variational methods for the construction of breathers, i.e., polychromatic, spatially localized and time-periodic solutions of nonlinear wave equations.

The results were obtained in collaboration with D. Scheider and T. Yesil.