中文摘要：

文中以在众多领域中存在广泛应用的变系数函数5阶Korteweg—de Vries方程为研究对象，首先基于Ablowitz—Kaup—Newell—Segur系统推出方程存在孤子解的约束条件和Lax对，进而构造方程的自-Backlund变换和孤子解，并分析讨论变系数函数对孤子解传播特征的影响．

英文摘要：

A variable-coefficient fifth-order Korteweg-de Vries equation is investigated in this paper, which has a wide range of application in physics and engineering fields. Using the Ablowitz-Kaup-Newell-Segur system, the constraint for this model to have soliton solutions and Lax pair are derived. Moreover, the auto-Backlund trans- formation and solitonic solution are constructed. The influence of the variable-coefficient functions on propagation characteristics of the one solitonie solution is presented.