Decay estimates for one-dimensional wave equations with inverse power potentials

We study the one-dimensional wave equation with an inverse power potential that equals const.x^−m for large |x|, where m is any positive integer greater than or equal to 3. We show that the solution decays pointwise like t^−m for large t, which is consistent with existing mathematical and physical literature under slightly different assumptions. Our results can be generalized to potentials consisting of a finite sum of inverse powers, the largest of which being const.x^−α, where α > 2 is a real number, as well as potentials of the form const.x^−m+O(x^−m−δ1) with δ₁ > 3.