On the Cauchy problem and peakons of a two-component Novikov system  

作　　者：Changzheng Qu Ying Fu 

机构地区：[1]School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China [2]School of Mathematics,Northwest University,Xi’an 710127,China

出　　处：《Science China Mathematics》2020年第10期1965-1996,共32页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11631007,11471174 and 11471259)。

摘　　要：We study a two-component Novikov system,which is integrable and can be viewed as a twocomponent generalization of the Novikov equation with cubic nonlinearity.The primary goal of this paper is to understand how multi-component equations,nonlinear dispersive terms and other nonlinear terms affect the dispersive dynamics and the structure of the peaked solitons.We establish the local well-posedness of the Cauchy problem in Besov spaces B^s/p,r with 1 p,r+∞,s>max{1+1/p,3/2}and Sobolev spaces H^s(R)with s>3/2,and the method is based on the estimates for transport equations and new invariant properties of the system.Furthermore,the blow-up and wave-breaking phenomena of solutions to the Cauchy problem are studied.A blow-up criterion on solutions of the Cauchy problem is demonstrated.In addition,we show that this system admits single-peaked solitons and multi-peaked solitons on the whole line,and the single-peaked solitons on the circle,which are the weak solutions in both senses of the usual weak form and the weak Lax-pair form of the system.

关 键 词：two-component Novikov system Hamiltonian structure Camassa-Holm type equation WELLPOSEDNESS peaked soliton 

分 类 号：O175[理学—数学]