Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909776515956736 |
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| author | Plachenov, Alexandr B. Kiselev, Aleksei P. |
| author_facet | Plachenov, Alexandr B. Kiselev, Aleksei P. |
| contents | A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0, where z is a Cartesian coordinate, and has an additional factor logarithmic with respect to the distance as z > 0. Asymptotics for a point running to infinity with an arbitrary constant speed is discussed |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity Plachenov, Alexandr B. Kiselev, Aleksei P. Optics 78A40 A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0, where z is a Cartesian coordinate, and has an additional factor logarithmic with respect to the distance as z > 0. Asymptotics for a point running to infinity with an arbitrary constant speed is discussed |
| title | Asymptotics of a finite-energy unidirectional solution of the wave equation with non-spherical-wave behavior at infinity |
| topic | Optics 78A40 |
| url | https://arxiv.org/abs/2509.00773 |