广义Vakhnenko方程的周期圈波和圈孤子解

The Periodic Loop-wave Solution and Loop Soliton Solution of the Generalized Vakhnenko Equation

本文用动力系统方平面分支方法，研究一个广义Vakhnenko方程的圈波．在p=3的参数条件下，获得了精确的周期圈波和圈孤子解的表达式，作出了周期圈波和圈孤子的平面图形，直观的显示了这两种解的动力学性质．本文的结果丰富了广义Vakhnenko方程的研究．

In this paper, the loop wave solution of a generalized Vakhnenko equation has been studied by using planar bifurcation method of dynamic system. As a result, under β = 3, the representations of periodic loop-wave solution and loop soliton solution are given, as well their planar graphs. These results are useful supplement to investigation of Vakhnenko equation.