TWO HIERARCHIES OF NONLINEAR SOLITON EQUATIONS, NEW INTEGRABLE SYMPLECTIC MAP AND DISCRETE INTEGRABLE COUPLINGS

Two hierarchies of nonlinear soliton equations are derived from a discrete spectral problem. It is shown that the hierarchies are completely integrable Hamiltonian systems. Moreover, a new integrable symplectic map is obtained using the binary nonlinearization method. With the help of semi-direct sum of Lie algebra, discrete integrable couplings are constructed.