Some generalized isospectral-nonisospectral integrable hierarchies

Abstract

Abstract 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 .