【摘要】 特征列方法将方程的零点集转化为几个特征列,即不可约的三角列的零点集的并集,使得方程达到降阶、降维度数的目的;李对称则提供了一套系统的方法,通过对对称约化和群不变解研究,方程阶数大大降低。这两种方法的共同之处在于其思想都是通过变换将原方程化为更易求解的同解方程(组),减少求解方程的计算量。将这两种方法有效结合,应用微分-差分特征列法将耦合的Toda晶格方程分解,对分解得到的特征列集应用差分Lie对称法,求得这些特征列集的不变群和群不变解。根据零点分解定理,这些特征列集的群不变解就是耦合Toda晶格方程的群不变解。更多还原

【Abstract】 The characteristic series method will convert the zero set of equation to the union of zero sets of characteristic series, which is irreducible triangular series. This guarantees that the degree and dimension of the equations can be reduced. Lie symmetry provides a systematic approach to reduce the degree of the equations by studying the symmetry reduction and group invariant solution. Both of the two methods have the same purpose that is to reduce the equations into some simple equations with lower degree and dimension, to reduce the calculation of solving the equations. The zero decomposition theorem is used to divide the coupled Toda lattice equations, and the invariant groups and group invariant solutions of the characteristic series are obtained by Lie symmetry method. According to the zero decomposition theorem, the group invariant solutions of the characteristic series and the coupled Toda lattice equations are the same.更多还原