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

2022/11/17 by Abdon Moutinho, Moutinho, Abdon
Computer Science · Engineering · Physics and Astronomy · #Advanced Fiber Optic Sensors #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.2211.09714

openalex publication_date 2022/11/17 · openalex created_date 2022/11/26 · openalex updated_date 2026/07/28

Abstract

This manuscript is the first of a series of two papers that study 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. In this paper, we construct a sequence of approximate solutions (ϕ_k(v,t,x))_k∈ℕ_{≥ 2} for this nonlinear wave equation such that each function ϕ_k(v,t,x) converges in the energy norm to the traveling kink-kink with speed v when t goes to +∞. The methods used in this paper are not restricted only to the ϕ⁶ model.

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