Ito方程组的对称分析与守恒律

Symmetry analysis and conservation law of Ito equations

基于Lie群分析方法,得到了Ito方程组的一维子代数最优系统和相似约化系统,并借助Ibragimov的新守恒定理成功构造出该方程组的3个守恒律。结果表明:这些揭示了Ito方程组对称与守恒律之间的内在联系,而且克服了Nöether定理的局限性,对研究Ito方程组的相关属性方面具有重要意义。

Based on the Lie group analysis method,a one-dimensional subalgebraic optimal system and a similar reduced system of Ito equations are obtained,and three conservation laws for the equations are successfully constructed with the help of Ibragimov's new conservation theorem.The results show the intrinsic connection between the symmetry and conservation laws of the system of Ito equations,and overcome the limitation of Nöether's theorem,which is important for studying the relevant properties of the system of Ito equations.