ANALYTICITY, GEVREY REGULARITY AND UNIQUE CONTINUATION FOR AN INTEGRABLE MULTI-COMPONENT PEAKON SYSTEM WITH AN ARBITRARY POLYNOMIAL FUNCTION

作者：Hu, Qiaoyi^*; Qiao, Zhijun^*

来源：Discrete and Continuous Dynamical Systems, 2016, 36(12): 6975-7000.

DOI：10.3934/dcds.2016103

• Analyticity
• Gevrey regularity
• unique continuation
• integrable system
• peakon

In this paper, we study the Cauchy problem for an integrable multi-component (2N-component) peakon system which is involved in an arbitrary polynomial function. Based on a generalized Ovsyannikov type theorem, we first prove the existence and uniqueness of solutions for the system in the Gevrey-Sobolev spaces with the lower bound of the lifespan. Then we show the continuity of the data-to-solution map for the system. Furthermore, by introducing a family of continuous diffeomorphisms of a line and utilizing the fine structure of the system, we demonstrate the system exhibits unique continuation.

• 出版日期2016-12
• 单位华南农业大学