时间分数阶Bogovavlenskii Kdv方程组的对称分析、精确解和守恒律  

Lie symmetry analysis, explicit solutions and conservation laws for the time fractional coupled Bogoyavlenskii KdV equations

作　　者：尹琦琦 冯滨鲁[2] 张玉峰 YIN Qi-qi;FENG Bin-Lu;ZHANG Yu-feng(China University of Mining and Technology, Xuzhou, 221116, China;Weifang University, Weifang 261061, China)

机构地区：[1]中国矿业大学数学学院,江苏徐州221116 [2]潍坊学院数学与信息科学学院,山东潍坊261061

出　　处：《潍坊学院学报》2018年第6期1-9,共9页Journal of Weifang University

基　　金：supported by the Fundamental Research Funds for the Central University(No.2017XKZD11)

摘　　要：本文主要对分数阶Bogoyavlenskii KdV系统及其Riemann-Liouville(RL)导数进行了全面的研究,并得到了方程的幂级数形式解及其守恒律。首先,通过李对称分析方法研究了该系统的李点对称性和单参数变换群及相似变换,将Bogoyavlenskii KdV系统化为一类特殊的分数阶常微分方程系统(ODE)。该简化系统是在Erdelyi Kober(EK)意义上定义的。其次,采用幂级数展开法求解了得到的分数阶常微分方程组。最后,应用新的守恒定理和Noether算子的推广,构造了Bogoyavlenskii KdV系统的非局部守恒律。In this paper, the power series solution and conservation laws have been obtained by Lie symmetries study for fractional dierential equations with Riemann-Liouville(RL) derivative. In this paper, we obtain point symmetries, similarity variables,similarity transformation and reduce the governing equation to a special system of ordinary dierential equation(ODE) of fractional order. The reduced equation is in the Erdelyi-Kober(EK) sense. Then, we solve the reduced system of ODE using the power series(PS) expansion method. The new conservation theorem and the generalization of the Noether operators are applied to construct nonlocal conservation laws(CLs) for the generalized KdV equations.

关 键 词：分数阶微分方程组 李对称分析 幂级数展开法 守恒律 

分 类 号：TM923[电气工程—电力电子与电力传动]