耦合KdV方程的几个精确解

Exact Solutions of Coupled KdV Equation

Darboux变换是求孤子方程的精确解的一种新方法。它借助于孤子方程的Lax对。从方程的平凡解导出新的非平凡解。本文对一个四阶特征值问题找出了Darboux变换,并由此得到耦合KdV方程的孤子解,周期解,极点解等。

For Coupled KdV equation The following theorem is obtained. Theorem: If(U,V, W) is asolution of(1), φ is a general solution of (2), and is a special solution of (2). Then, the following (U_1, V_1, W_1) is also a solution of(1), and φ_1 is a general solution of (2)with potentials (U_1, V_1, W_1); φ_1=φ_x-(Ln )_xφ; U_1=U+2(Ln )_(xx); V_I=V-U-_(xx)/; (Darboux Transformation) By means of the theorem we get some exact solutions of (1) from a trival solution are gived, such as soliton solustion, periodic solution, rational solution,φetc..