2025/12/01 by Jun Wu, Yue Liu, Wu, Jun +3
Mathematics · Physics and Astronomy · #35B35 #35B40 #35Q51 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2512.01225
openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
We establish the asymptotic stability of lefton solutions-exponentially localized stationary solitary waves-for the b-family of equations with positive momentum density in the regime b < -1. Unlike the completely integrable Camassa-Holm (b=2) and Degasperis-Procesi (b=3) cases, this parameter range lies outside integrability and exhibits distinct nonlinear dynamics. Our analysis adapts the Martel-Merle framework for generalized KdV equations to the nonlocal, non-integrable structure of the b-family of equations. The proof combines a nonlinear Liouville property for solutions localized near leftons with a refined spectral analysis of the associated linearized operator. These results provide the first rigorous asymptotic stability theory for leftons in the non-integrable b-family of equations.