2022/11/17 by Moutinho, Abdon
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2211.09749
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 ϕ6 model. We prove for any k∈ℕ that if the incoming speed v is small enough, then, after the collision, the two kinks will move away with a velocity vf such that \vert vf-v\vert≤ vk and the energy of the remainder will also be smaller than vk. This manuscript is the continuation of our previous paper where we constructed a sequence ϕk of approximate solutions for the ϕ6 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.