A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails
Numerical Analysis
2025-11-05 v2 Numerical Analysis
Mathematical Physics
Analysis of PDEs
math.MP
Abstract
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.
Cite
@article{arxiv.2507.00674,
title = {A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails},
author = {Oliver Rinne},
journal= {arXiv preprint arXiv:2507.00674},
year = {2025}
}
Comments
24 pages, 10 figures, 2 tables. Additional convergence tests, extended introduction and several minor changes. To appear in Nonlinearity