Narrow Results

In this paper, we first introduce a nonisospectral problem associate with a loop algebra. Based on the nonisospectral problem, we deduce a nonisospectral integrable hierarchy by solving a nonisospectral zero curvature equation. It follows that the standard AKNS hierarchy and KN hierarchy are obtained by reducing the resulting nonisospectral hierarchy. Then, the Hamiltonian system of the resulting nonisospectral hierarchy is investigated based on the trace identity. Additionally, an extended integrable system of the resulting nonisospectral hierarchy is worked out based on an expanded higher-dimensional Loop algebra.

We study irreducible modules for map Heisenberg–Virasoro algebras. In particular, we give a complete classification of irreducible Harish–Chandra modules for map Heisenberg–Virasoro algebras. We will also classify non-weight irreducible modules for map Heisenberg–Virasoro algebras whose restriction on the degree zero part of the universal enveloping algebra of Witt algebra is free of rank 1.

Under the frame of the (2 + 1)-dimensional zero curvature equation and Tu model, the (2 + 1)-dimensional TD hierarchy is obtained. Again, by using the expanding loop algebra, the integrable coupling system of the above hierarchy is given.