Approximate kink-kink solutions for the ϕ6 model in the low-speed limit

Article type: Research Article

Authors: Moutinho, Abdon^{; *; **}

Affiliations: Georgia Tech, 686 Cherry St NW, Atlanta, GA 30332, USA

Correspondence: [**] Corresponding author. E-mail: aneto8@gatech.edu.

Note: [*] Current address: Georgia Tech, 686 Cherry St NW, Atlanta, GA 30332, USA.

Abstract: In this paper, we consider the problem of elasticity and stability of the collision of two kinks with low speed v for the nonlinear wave equation known as the ϕ6 model in dimension 1+1. We construct a sequence of approximate solutions (ϕk(v,t,x))k∈N⩾2 for this model to understand the effects of the collision in the movement of each soliton during a large time interval. The construction uses a new asymptotic method which is not only restricted to the ϕ6 model.

Keywords: Kink, soliton, ϕ⁶ model, non-integrable model, scalar field, partial differential equation, ordinary differential equation, collision

DOI: 10.3233/ASY-241917

Journal: Asymptotic Analysis, vol. 140, no. 3-4, pp. 191-280, 2024