2016/08/14 by Diego Catalano Ferraioli, Ferraioli, Diego Catalano, Igor Leite Freire +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1608.04604
openalex publication_date 2016/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce a two-component system, depending on a parameter b, which generalises the Camassa-Holm (b=1) and Novikov equations (b=2). By investigating its Lie algebra of classical and higher symmetries up to order 3, we found that for b≠ 2 the system admits a 3-dimensional algebra of point symmetries and apparently no higher symmetries, whereas for b=2 it has a 6-dimensional algebra of point symmetries and also higher order symmetries. Also we provide all conservation laws, with first order characteristics, which are admitted by the system for b=1,2. In addition, for b=2, we show that the system is a particular instance of a more general system which admits an \mathfraksl(3,ℝ)-valued zero-curvature representation. Finally, we found that the system admits peakon solutions and, in particular, for b=2 there exist 1-peakon solutions with non-constant amplitude.