A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918185491496960 |
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| author | Rinne, Oliver |
| author_facet | Rinne, Oliver |
| contents | We consider the scalar wave equation with power nonlinearity in n+1 dimensions. Unlike most previous numerical studies, we go beyond the radial case and do not assume any symmetries for n=3, and we only impose an SO(n-1) symmetry in higher dimensions. Our method is based on a hyperboloidal foliation of Minkowski spacetime and conformal compactification. We focus on the late-time power-law decay (tails) of the solutions and compute decay exponents for different spherical harmonic modes, for subcritical, critical and supercritical, focusing and defocusing nonlinear wave equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_00674 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails Rinne, Oliver Numerical Analysis Mathematical Physics Analysis of PDEs We consider the scalar wave equation with power nonlinearity in n+1 dimensions. Unlike most previous numerical studies, we go beyond the radial case and do not assume any symmetries for n=3, and we only impose an SO(n-1) symmetry in higher dimensions. Our method is based on a hyperboloidal foliation of Minkowski spacetime and conformal compactification. We focus on the late-time power-law decay (tails) of the solutions and compute decay exponents for different spherical harmonic modes, for subcritical, critical and supercritical, focusing and defocusing nonlinear wave equations. |
| title | A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails |
| topic | Numerical Analysis Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2507.00674 |