Travelling waves for Maxwell’s equations in nonlinear and symmetric media

Abstract

We look for travelling wave fields $E(x,y,z,t)=U(x,y)cos(kz+\omega t)+\tilde{U}(x,y)sin(kz+\omega t),(x,y,z)\in R^3,t\in R,$satisfying Maxwell’s equations in a nonlinear and cylindrically symmetric medium. We obtain a sequence of solutions with diverging energy consisting of transverse magnetic field modes. In addition, we consider a general nonlinearity, controlled by an N-function.