耦合非线性Schrdinger方程的Darboux变换及精确解

Darboux Transformation and Explicit Solutions of the Couple Nonlinear Schrdinger Equation

Darboux变换方法是求解非线性微分方程的最有效的方法之一.通过研究一个3×3矩阵谱问题,利用谱问题的规范变换,为耦合非线性Schrdinger方程建立了Darboux变换,并求出了该方程的精确解.

In the field of finding the explicit solutions of nonlinear differential equations, Darboux transformation is regarded as one of the most effective ways. Through the intensive study of a 3 × 3 matrix spectral problem, with the help of a gauge transformation of a spectral problem, a Darboux transformation of the couple nonlinear Schrodinger equations is obtained. Furthermore, the explicit solutions of the equations are also given.