Asymptotic stability of the fourth order ϕ⁴ kink for general perturbations in the energy space

2023/05/30 by Christopher Maulén, Claudio Muñoz, Maulén, Christopher +1 · 1 citation
Mathematics · Physics and Astronomy · #35B40 #35L76 #37K40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2305.19222

openalex publication_date 2023/05/30 · openalex created_date 2023/06/01 · openalex updated_date 2026/08/01

Abstract

The Fourth order ϕ⁴ model generalizes the classical ϕ⁴ model of quantum field theory, sharing the same kink solution. It is also the dispersive counterpart of the well-known parabolic Cahn-Hilliard equation. Mathematically speaking, the kink is characterized by a fourth-order nonnegative linear operator with a simple kernel at the origin but no spectral gap. In this paper, we consider the kink of this theory, and prove orbital and asymptotic stability for any perturbation in the energy space.

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