中文摘要：

研究有限深分层流体有限振幅内孤立波的高阶理论。针对上层流体密度均匀，下层密度随深度变化的有限深混合分层模型，采用PLK方法和匹配渐近展开法相结合，建立了波幅的二阶、三阶修正所满足的方程。并在特殊密度分布——强分层流体模型下对波幅二阶、三阶发展方程进行了数值计算，得到了波幅二阶、三阶解曲线。结果表明，我们的一阶、二阶振幅修正方程与前人研究结果一致，二阶、三阶解曲线相对于一阶解曲线有明显的改进，因此，推广了前人的工作。

英文摘要：

The solitary waves with finite amplitude and in stratified fluids with finite depth, in which the density varies with depth in lower layer but keeps uniform in upper layer, are investigated. By combining the PLK method with the matching of asymptotic expansions, second and third-order amplitude evolution equation are derived for cases with general density profile. And then, the curves of the second and third-order equations for special density profile--strong stratification are drawn. It is found that the first and second-order evolution equation are consistent with the known ones, the second and third-order curves are improved more evidently than the first-order one and hence predecessors＇ work has been extended.