微分算子的划分、相关关系和达布变换
Division of Differential operators, intertwine relations and Darboux Transformations
摘要：
利用非交换微分酉环的广义Bell多项式解决了微分算子的左、右可除问题。多项式的定义是通过递归关系来实现的。给出了经典Bell polinomil的广义Polinomil表达式。精确因子分解可能性的条件导致互逆关系，并导致一些可线性化的广义Burgers方程。本文给出了Matveev定理的另一种证明，并由互逆关系导出了系数的Darboux-Matveev变换公式，该公式也表示为广义Bell多项式。
英文摘要：
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The expresions of classic Bell polinomils via generalized one is given. The conditions of an exact factorization possibility leads to the intertwine relation and results in some linearizable generalized Burgers equation. An alternative proof of the Matveev theorem is given and Darboux - Matveev transformations formula for coefficients follows from the intertwine relations and also expressed in the generalized Bell polinomials.
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