Travelling waves for Maxwell's equations in nonlinear and symmetric media
Abstract
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R}, $$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.01433
- arXiv:
- arXiv:2406.01433
- Bibcode:
- 2024arXiv240601433M
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 18 pages