In this article, with the aid of the Lie algebra $A_1$ composed of second order matrices and Lie algebra $A_2$ composed of third order matrices, some new soliton hierarchies of evolution equations are deduced and the corresponding Hamiltonian structures are also worked out by utilizing the trace identity. Specially, one of the integrable soliton hierarchicy is reduced to the generalized Fokker–Plank equation (gFP) and special bond pricing equation. Next, the nonlinear self-adjointness of the generalized Fokker–Plank equation is verified and conservation laws are constructed with the aid of Ibragimov’ method. Moreover, we investigate the coverings and the nonlocal symmetries of the generalized Fokker–Plank equation by applying the classical Frobenius theorem and the coordinates of a infinitely-dimensional manifold in the form of Cartesian product. Besides, we apply the Li’s method to obtain two basic Darboux transformations of (gFP) with two different forms of $T$.

在本文中，借助李代数 ${\mathrm{一种}}_{\mathrm{1个}}$ 由二阶矩阵和李代数组成 ${\mathrm{一种}}_{\mathrm{2个}}$由三阶矩阵组成，推导了一些新的演化方程孤子层次，并利用迹身份确定了相应的哈密顿结构。特别地，可积孤子层次结构之一简化为广义的Fokker-Plank方程（gFP）和特殊债券定价方程。接下来，验证了广义Fokker-Plank方程的非线性自伴性，并借助Ibragimov'方法构造了守恒律。此外，我们通过应用经典Frobenius定理和笛卡尔积形式的无穷维流形的坐标，研究广义Fokker-Plank方程的覆盖和非局部对称性。除了，$Ť$。