Orbital stability of two-component peakons  

作　　者：Cheng He Xiaochuan Liu Changzheng Qu 

机构地区：[1]School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China [2]School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China

出　　处：《Science China Mathematics》2023年第7期1395-1428,共34页中国科学：数学（英文版）

基　　金：National Natural Science Foundation of China(Grants Nos.12271424 and 11871395);National Natural Science Foundation of China(Grants Nos.11971251,11631007 and 12111530003)。

摘　　要：We prove that the two-component peakon solutions are orbitally stable in the energy space.The system concerned here is a two-component Novikov system,which is an integrable multi-component extension of the integrable Novikov equation.We improve the method for the scalar peakons to the two-component case with genuine nonlinear interactions by establishing optimal inequalities for the conserved quantities involving the coupled structures.Moreover,we also establish the orbital stability for the train-profiles of these two-component peakons by using the refined analysis based on monotonicity of the local energy and an induction method.

关 键 词：Novikov equation two-component Novikov system peakons orbital stability conservation law Camassa-Holm equation 

分 类 号：O175[理学—数学]