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This talk 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 arc found by using Cosgroves 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.