Two types of loop algebras and their expanding Lax integrable models

摘要

Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation Ut-Vx+[U,V]=0,but in this paper,a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials.Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator (J) is presented by constructing a subalgebra (G) of the loop algebra (A)2.As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers,their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.