【摘要】 通过介绍一个含四个位势的4×4矩阵谱问题,得到一个新的非线性发展方程族,其中较有意义的一个方程是耦合Kaup-Newell方程.利用迹恒等式,得到了它的双哈密顿结构.在某个约束条件下,通过特征值问题的非线性化方法,得到了Liouville意义下耦合Kaup-Newell方程新的可积分解.更多还原

【Abstract】 By introducing a 4 x 4 matrix spectral problem with four potentials,a hierarchy of nonlinear evolution equations are derived,an interesting equation in the hierarchy is a coupled Kaup-Newell equation.The 2-Hamiltonian structures are presented with the aid of the trace identity.Through the nonlinearization of eigen value problems and an additional constraint,a new integrable decomposition of the coupled Kaup-Newell equation is presented in the sense of Liouville.更多还原