中文摘要：

利用Darboux变换求解（2＋1）维MKdV方程的孤子解.先从广义MKdV方程的谱问题出发,推导出（2＋1）维MKdV方程及其对应的Lax对;再借助零曲率方程构造（2＋1）维MKdV方程3种不同的Darboux变换,并讨论了3种Darboux变换间的关系.作为应用,求出了（2＋1）维MKdV方程的孤子解,并给出了孤子解的碰撞情形.

英文摘要：

Soliton solutions of（2＋1） dimensional MKdV equation were obtained via Darboux transformation.Based on spectral problems of the generalized MKdV equation,a（2＋1） dimensional MKdV equation and its Lax pairs were derived.With the help of zero curvature equation,three different Darboux transformations（DTs） of the（2＋1） dimensional MKdV equations were constructed.Then,relations among three Darboux transformations were discussed.As an example of application of DT,soliton solutions of（2＋1） dimensional MKdV equation were given and various collision graphics were discussed.