(3+1)维时间分数阶KdV-Zakharov-Kuznetsov方程的分支分析及其行波解

Dynamical Analysis and Solutions for (3+1)-Dimensional Time Fractional KdV-Zakharov-Kuznetsov Equations

首先,运用拟设方法和动力系统分支方法,获得了(3+1)维时间分数阶KdV-Zakharov-Kuznetsov方程的奇异孤子解、亮孤子解、拓扑孤子解、周期爆破波解、孤立波解等.再利用MAPLE软件画出了KdV-Zakharov-Kuznetsov方程在不同条件下的分支相图.最后,讨论了行波解之间的联系.

By means of the ansatz method and the bifurcation analysis,the singular soliton solution,the bright soliton solution,the topological soliton solution,the periodic explosive solution and the solitary wave solution of the(3+1)-dimensional time fractional KdV-Zakharov-Kuznetsov equations were constructed.In addition,the phase portraits of KdV-Zakharov-Kuznetsov equations were obtained for various cases with the MAPLE software.Finally,the relationships among travelling wave solutions were discussed.