一个扩展的r矩阵及其应用

摘要

发展并应用孤立子方程的谱问题非线性化方法到对称矩阵Kaup－Newell方程上。得到了一个扩展的r矩阵，并应用r矩阵方法证明了对称矩阵kaup－Newell方程的有限维Hamilton系统是Liouville完全可积的。%The approach of nonlinearization of spectral problem is extended and applied to the symmetric matrix Kaup-Newell equation .An extended r-matrix formula is presented .The complete integrability in the Liouville sense of the finite dimensional Hamiltonian system which results from the symmetric matrix Kaup -Newell equation is established in the framework of r -matrix.