Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.
For the energy balance, we set the nonlinear term to zero and evolve the linear equation in both coordinate systems
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Semilinear wave equations in homothetic hyperboloidal coordinates and tail decay
Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.