Internal degrees of freedom, long-range interactions and nonlocal effects in perturbed Klein-Gordon equations

► The number of soliton internal modes can depend on the asymptotic behavior of the kink solution. ► Internal modes can exist if the external perturbation is not localized. ► Internal modes can exist if the external perturbation behaves as a power-law. ► The kink solutions can exhibit a power-law asymptotic behavior.