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

Abstract

We look for travelling wave fields $$E(x,y,z,t)=U(x,y)\cos (kz+\omega t)+\tilde{U}(x,y)\sin (kz+\omega t),(x,y,z)\in {\mathbb{R}}^3,t\in \mathbb{R},$$ satisfying Maxwell's equations in a nonlinear and cylindrically symmetric medium. We obtain a sequence of solutions with diverging energy that is different from that obtained by McLeod, Stuart, and Troy. In addition, we consider a more general nonlinearity, controlled by an \textit{N}-function.

arXiv comment20 pages, minor improvements

References in corpus (2)

• Ground and bound state solutions of semilinear time-harmonic Maxwell equations in a bounded domain
• Multiple solutions to a nonlinear curl-curl problem in ${\mathbb{R}}^3$