A general coupled KdV equation, which describes the interactions of two long waves with different dispersion relation, is considered. By employing the Hirota’s bilinear method, the bilinear form is obtained, and the one-soliton solution and two-soliton solution are constructed. Moreover, the elasticity of the collision between two solitons is proved by analyzing the asymptotic behavior of the two-soliton solution. Some figures are displayed to illustrate the process of elastic collision.

中文翻译：

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一般耦合KdV方程的孤子解和长时间渐近分析

考虑了一个通用的耦合KdV方程，该方程描述了两个具有不同色散关系的长波的相互作用。利用Hirota的双线性方法，得到双线性形式，并构造了一个单孤子解和两个孤子解。此外，通过分析两个孤子解的渐近行为，证明了两个孤子之间的碰撞弹性。显示一些图以说明弹性碰撞的过程。