Si. Zaki et al., NUMERICAL SIMULATIONS OF KLEIN-GORDON SOLITARY-WAVE INTERACTIONS, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 112(7), 1997, pp. 1027-1036
Solutions of a non-linear Klein-Gordon equation are studied numericall
y using a cubic B-spline finite-element method. Test results indicate
that, when solitary waves interact, the final state obtained depends o
n their relative velocity. The simulations confirm existing observatio
ns and produce new results. The numerical algorithm developed is effic
ient with an undemanding stability criterion.