【摘要】 本文首先构造了Loop代数A3的一个特殊子代数G,使和其二个子代数G1,G2满足关系G=G1(?)G2。利用G1构造一个等谱问题;再利用屠格式得到一个具有双Hamilton结构的新的孤子方程族。其次,利用G1的基元的线性组合,得到了一个另一类Loop代数G1,由此再利用屠格式获得第二类新的可积系。最后,由可积耦合理论,得到第一个孤子族的可积耦合系统。类似地,构造了Loop代数A3的子代数G1的一个扩展Loop代数G,获得第二孤子族的可积耦合。更多还原

【Abstract】 A special subalgebra G of the Loop algebra A3 is constructed first, so that two subalgebras G1 and G2 of Loop algebra G satisfy the relation G=G1(?)G2. By making use of the G1, an isospectral problem is established. Again by the use of Tu scheme, a new integrable hierarchy of soliton equations with bi-Hamiltonian structure is obtained. Second, by employing a proper linear combination of the basis of the Loop algebra G1, another Loop algebra G1 is presented. It follows that the second type of new integrable system is given via Tu scheme. Finally, in terms of the theory of integrable couplings, the integrable coupling of the first kind of integrable hierarchy is engendered. Similarly, by constructing an expanding Loop algebra G of the subalgebra G1, for the Loop algebra A3, the integrable coupling of the second soliton hierarchy may be worked out.更多还原