This paper is devoted to studying a two-component peakon system with cubic nonlinearity, which is a two-component extension of the cubic Camassa–Holm equation. We first discuss the local well-posedness for the Cauchy problem of the system. Then, in light of a fine structure of the system, we present the precise blow-up scenario for strong solutions to the system and derive a new blow-up result with respect to initial data. Finally, peakon solutions are discussed as well.
Shaojie Yang and Zhijun Qiao , "Qualitative analysis for a two-component peakon system with cubic nonlinearity", J. Math. Phys. 63, 121504 (2022) https://doi.org/10.1063/5.0123524
Journal of Mathematical Physics
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