A new generalised two-component Camassa-Holm type system with waltzing peakons and wave breaking

作者：Yang, Li^*; Zhang, Baoshuai; Zhou, Shouming

来源：Nodea-Nonlinear Differential Equations and Applications, 2018, 25(4): 37.

DOI：10.1007/s00030-018-0528-4

• Generalized Camassa-Holm type system
• Besov spaces
• Well-posedness
• Blow-up
• Waltzing peakons

This paper mainly investigate the Cauchy problem for the generalised two-component Camassa-Holm type system, which includes the celebrated Camassa-Holm equation, Degasperis equation, Novikov equation, and the two-component cross-coupled Camassa-Holm system, Novikov system as special cases. Firstly, the local well-posedness of the system in nonhomogeneous Besov spaces B-l,r(s)(R) x B-l,r(s)(R) with l, r is an element of [1, infinity], s > max{2+ 1/l, 5/2} is established by using the Littlewood-Paley theory and transport equations theory. Moreover, we verify the blow-up occurs for this system only in the form of breaking waves. Finally, the waltzing peakons for the system and some numerical experiments to illustrate our results are performed.

• 出版日期2018-8
• 单位重庆师范大学