摘要
An invariant function （IF） is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary （l q-1）-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions.
作者
Sen-Yue Lou
Ruo-Xia Yao
楼森岳;姚若侠(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;School of Computer Science, Shaanxi Normal University)
基金
Supported by the National Natural Science Foundations of China under Grant Nos.11435005,11471004,11175092,and 11205092
Shanghai Knowledge Service Platform for Trustworthy Internet of Things No.ZF1213
K.C.Wong Magna Fund in Ningbo University
