A New Approach for Generating the TX Hierarchy as well as Its Integrable Couplings - Guangming Wang (Abstract and Applied Analysis)
Tu Guizhang and Xu Baozhi once introduced an isospectral problem by a loop algebra with degree being λ, for which an integrable hierarchy of evolution equations (called the TX hierarchy) was derived under the frame of zero curvature equations. In the paper, we present a loop algebra whose degrees are 2λ and 2λ+1 to simply represent the above isospectral matrix and easily derive the TX hierarchy. Specially, through enlarging the loop algebra with 3 dimensions to 6 dimensions, we generate a new integrable coupling of the TX hierarchy and its corresponding Hamiltonian structure.