Georgia Institute of Technology College of Sciences

We will talk about our results on the elasticity and stability of the 
collision of two kinks with low speed v>0 for the nonlinear wave 
equation of dimension 1+1 known as the phi^6 model. We will show that 
the collision of the two solitons is "almost" elastic and that, after 
the collision, the size of the energy norm of the remainder and the size 
of the defect of the speed of each soliton can be, for any k>0, of the 
order of any monomial v^{k} if v is small enough.

References:
This talk is based on our current works:
On the collision problem of two kinks for the phi^6 model with low speed 
   [https://arxiv.org/abs/2211.09749]
Approximate kink-kink solutions for the phi^6 model in the low-speed 
limit [https://arxiv.org/abs/2211.09714]