摘要
The dark Korteweg-de Vries （KdV） systems are defined and classified by Kupershmidt sixteen years ago. However, there is no other classifications for other kinds of nonlinear systems. In this paper, a complete scalar classification for dark modified KdV （MKdV） systems is obtained by requiring the existence of higher order differential polynomial symmetries. Different to the nine classes of the dark KdV case, there exist twelve independent classes of the dark MKdV equations. Fhrthermore, for the every class of dark MKdV system, there is a free parameter. Only for a fixed parameter, the dark MKdV can be related to dark KdV via suitable Miura transformation. The reeursion operators of two classes of dark MKdV systems are also given.
作者
Na Xiong
Sen-Yue Lou
Biao Li
Yong Chen
熊娜;楼森岳;李彪;陈勇(Shanghai Key Laboratory of Trustworthy Computing, East China Normal University;Ningbo Collabrative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere, and Faculty of Science,Ningbo University)
基金
Supported by the Global Change Research Program of China under Grant No.2015Cb953904
National Natural Science Foundation of China under Grant Nos.11675054,11435005,11175092,and 11205092
Shanghai Knowledge Service Platform for Trustworthy Internet of Things(No.ZF1213)
K.C.Wong Magna Fund in Ningbo University
