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

2024/06/03 by Mederski, Jarosław, Schino, Jacopo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.01433

Abstract

We look for travelling wave fields E(x,y,z,t)= U(x,y) cos(kz+ωt)+ \widetilde U(x,y)sin(kz+ωt), (x,y,z)∈ℝ³, t∈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 N-function.

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