Year: 2025
Type: article
Abstract: 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 φ 6 model.We prove for any k ∈ ގ 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 φ k of approximate solutions for the φ 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.
Source: Analysis & PDE
Author: Abdon Moutinho
Institution: Georgia Institute of Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4414006956