Karlovich, Yu. I.; Komech, A. I.; Kopylova, E. A.; Merzon, A. E. On the spreading rate of the soliton perturbation for relativistic nonlinear wave equations. (English) Zbl 1259.35180 Commun. Math. Anal. 14, No. 2, 95-102 (2013). Summary: 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. MSC: 35Q51 Soliton equations 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 35B40 Asymptotic behavior of solutions to PDEs Keywords:relativistic nonlinear wave equation; soliton; weighted norms PDF BibTeX XML Cite \textit{Yu. I. Karlovich} et al., Commun. Math. Anal. 14, No. 2, 95--102 (2013; Zbl 1259.35180) Full Text: Euclid OpenURL