2025/12/15 by Kenneth H. Karlsen, Yan Rybalko, Karlsen, Kenneth H. +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2512.13305
openalex publication_date 2025/12/15 · openalex created_date 2025/12/17 · openalex updated_date 2026/07/28
We investigate the Cauchy problem for a two-component generalization of the Novikov equation with cubic nonlinearity -- an integrable system whose solutions may develop strong nonlinear phenomena such as gradient blow-up and interactions between peakon-like structures. Our study has two main objectives: first, to analyze the generic regularity of global conservative solutions; and second, to construct a new metric that guarantees the Lipschitz continuity of the flow. Building on the geometric framework developed by Bressan and Chen for quasilinear second-order wave equations, we prove that the solution retains Ck regularity away from a finite number of piecewise Ck-1 characteristic curves. Furthermore, we provide a description of the solution behavior in the vicinity of these curves. By introducing a Finsler norm on tangent vectors in the space of solutions, expressed in the transformed Bressan-Constantin variables, we introduce a Lipschitz metric representing the minimal energy transportation cost between two solutions.