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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01433 |
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| _version_ | 1866915556240654336 |
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| author | Mederski, Jarosław Schino, Jacopo |
| author_facet | Mederski, Jarosław Schino, Jacopo |
| contents | We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+ωt)+ \widetilde U(x,y)\sin(kz+ωt),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R}, $$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Travelling waves for Maxwell's equations in nonlinear and symmetric media Mederski, Jarosław Schino, Jacopo Analysis of PDEs We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+ωt)+ \widetilde U(x,y)\sin(kz+ωt),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R}, $$ 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. |
| title | Travelling waves for Maxwell's equations in nonlinear and symmetric media |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.01433 |