A hyperboloidal method for numerical simulations of multidimensional nonlinear wave equations: nonlinear tails

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.

24 pages, 10 figures, 2 tables. Additional convergence tests, extended introduction and several minor changes. To appear in Nonlinearity

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