Abstract: By use of a
-dimensional zero curvature equation and the AKNS spectral problem, a
-dimensional hierarchy of soliton equations is obtained. Again by employing a
subalgebra of the loop algebra the integrable coupling system of
the above hierarchy is presented. Finally, a multi-component loop algebra is constructed in terms of the
definition of the loop algebra and Jacobi identity, for which a multi-component
integrable hierarchy is given. The approach presented in the paper can be used
to other known isospectral problems.
Keywords and phrases: zero curvature equation, loop algebra, integrable system.
