【摘要】 本文将建立矩阵AKNS系列Darboux变换的行列式表示。为此,推广了Sylvester恒等式,并利用它化简Darboux迭带所致的行列式 最后,给出了几个著名的矩阵孤立子方程,如矩阵KdV、矩阵NLS、矩阵MKdV等的孤立子解。更多还原

【Abstract】 The determinant representation of the iterated Darboux Transforms of Matrix AKNS Hierarchy is established. To the purpose, the authors generalize the Sylvester Identity, and use it to simplify the complicated determinants appeared in the process of iterating Darboux transforms. At last, The authors give the soliton solutions of some famous matrix soliton equations such as matrix KdV equation, matrix NLS equation, matrix MKdV equation.更多还原