Asymmetric solutions for symmetric problems arising in Nonlinear Optics

Existence of asymmetric positive solutions for a class of symmetric nonlinear elliptic equations in R-N, N greater than or equal to 1 has been proved by using variational arguments. In the one-dimensional case such equation is a model in Nonlinear Optics aring in the study of asymmetric guided waves in a stratified dielectric medium. In dimension N = 2 the equation is a scalar approximation of a model arising from the study of propagation of a monochromatic electric field in optical cylindrical waveguides.