耦合KdV方程的约化及求解

Coupled KdV equation:similarity reduction and analytical solution

利用Clarkson和Kruskal(CK)直接方法,对耦合KdV方程进行相似约化,同时从李群出发对该约化方程作了群论解释.进一步地,借助Ablowitz-Ramani-Segur(ARS)算法对耦合方程展开Painlevé测试,找到了3个Painlevé可积模型.最后通过形变映射法,求得耦合KdV方程的准确解析解.

Using the CK direct method,we obtain the similarity reduction of coupled KdV equation,which is then explained in detail by group theory.To check the Painlevé integrability of coupled KdV equation,the reduction equation is also classified by means of the Painlevé test,and three types of P-integrable models are found.Finally,it is shown that the coupled KdV equation has kinds of traveling wave solutions,including conoidal periodic wave solution,soliton solution,and so on.