Asymptotics of Kink–Kink Interaction for Sine-Gordon Type Equations

We consider a class of semilinear wave equations with a small parameter $\varepsilon$. The nonlinearity of $F(u)$ is assumed to be such that the corresponding equation has an exact self-similar solution of kink type. For $F(u)$, we obtain sufficient conditions for two kinks to interact (in the sense of the leading term of the asymptotics with respect to $\varepsilon$) in the same way as the kinks of the sine-Gordon equation.