Propagation of nonlinear pulses near diffractive points of any order
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917450579181568 |
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| author | Wang, Jian Williams, Mark |
| author_facet | Wang, Jian Williams, Mark |
| contents | We construct pulse-type approximate solutions to nonlinear hyperbolic equations near diffractive points, allowing arbitrary (even infinite) order of grazing. We show that in low regularity spaces and the high frequency limit, such solutions can be approximated by a sum of incoming and reflected pulses constructed using incoming and reflected phases and profiles that satisfy transport equations. New low-regularity estimates comparing the size of pulses to the size of their profiles are required. Earlier geometric optics results for pulses assumed much higher regularity, and considered only propagation in free space or transversal reflection at boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27662 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Propagation of nonlinear pulses near diffractive points of any order Wang, Jian Williams, Mark Analysis of PDEs Classical Analysis and ODEs 35L20 We construct pulse-type approximate solutions to nonlinear hyperbolic equations near diffractive points, allowing arbitrary (even infinite) order of grazing. We show that in low regularity spaces and the high frequency limit, such solutions can be approximated by a sum of incoming and reflected pulses constructed using incoming and reflected phases and profiles that satisfy transport equations. New low-regularity estimates comparing the size of pulses to the size of their profiles are required. Earlier geometric optics results for pulses assumed much higher regularity, and considered only propagation in free space or transversal reflection at boundaries. |
| title | Propagation of nonlinear pulses near diffractive points of any order |
| topic | Analysis of PDEs Classical Analysis and ODEs 35L20 |
| url | https://arxiv.org/abs/2604.27662 |