The paper is devoted to four kinds of fifth-order nonlinear wave
equations including the Caudrey-Dodd-Gibbon equation, Kupershmidt
equation, Kaup-Kupershmidt equation and Sawada-Kotera equation. The
exact soliton solution and quasi-periodic solutions are found by
using Cosgrove's work and the method of dynamical systems. The
geometrical explanations of these solutions are also discussed. To
guarantee the existence of the above solutions, the parameter
conditions are determined.