利用Darboux变换对KdV方程孤子解普遍性质的讨论

Discussion of General Properties of Soliton Solutions of KdV Equation by Using Darboux Transformation

该文指出：利用Darboux变换不但可以非常简洁地得到文献［1］关于KdV方程单孤子解和双孤子解，而且便于讨论KdV方程的任意孤子解的性质．通过对KdV方程三孤子解的重点讨论，以及对KdV方程多孤子解的解析分析，得到了关于KdV方程任意阶孤子解的一些非常有意义的普遍结果．这些结果对于人们深入了解孤子相互作用规律具有重要的现实意义．

We point out that, by making use of Darboux trans formation, the analyticalform of one- and two-soliton solutions of KdV equation not only can be obtained concisely,but also the properties of any soliton solutions of KdV equation can be discussed easily.Through the detailed discussion of three-soliton solution and the analytical analysis of multisoliton solutions of KdV equation, we obtain some general and interesting conclusions aboutproperties for all soliton solutions of KdV equation. The conclusions would play an important role in the deep understanding of the law for interaction between solitons.