On the kink-kink collision problem for the ϕ6model with low speed

We study the elasticity of the collision of two kinks with an incoming low speed v (0, 1) for the nonlinear wave equation in dimension 1+1 known as the 6 model.We prove for any k that if the incoming speed v is small enough, then, after the collision, the two solitons move away with a velocity v f such that |v f -v| v k and the energy of the remainder will also be smaller than v k .This manuscript is the continuation of our previous paper where we constructed a sequence k of approximate solutions for the 6 model.The proof of our main result relies on the use of the set of approximate solutions from our previous work, modulation analysis, and a refined energy estimate method to evaluate the precision of our approximate solutions during a large time interval.The vacuum set V of the potential function U is the set U -1 {0} = {-1, 0, 1}.The unique constant solutions with finite energy of (1) are the functions of the form for any V.