We consider nonlinear relativistic wave equations in one space dimension and prove the spreading rate estimates for a general class of potentials. Such estimates play an important role in studying the asymptotic stability of solitons.
"On the Spreading Rate of the Soliton Perturbation for Relativistic Nonlinear Wave Equations." Commun. Math. Anal. 14 (2) 95 - 102, 2013.