一个求孤子方程有限带势解的方法

A Method to Seek the Finite-Band Solution of Soliton Equation

基于Lax对非线性化方法，我们以KdV方程为例给出了一个构造孤子方程的有限带势解的方法．通过Lax对非线性化KdV方程被分解成两个有限维可积系统，进而找到这些有限维可积系统公共的角-作用坐标，最终我们获得了KdV方程的有限带势解．

Based on the method of the nonlinearization of Lax pair, a method to seek the finite-band solution of solton equation is presented. We take KdV equation as an example. First through the nonlinearization of Lax pair, we decompose the KdV equation into two finite-dimensional integrable systems; then we give a common angle-action variables for these two Hamiltonian systems. Fanilly we obtain the finite-band solution of KdV equation.