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

摘要

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 , 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.