Truncated Painlevé Expansion And The Exact Travelling Wave Solutions To Nonlinear Evolution Equations

This dissertation mainly studies the methods in soliton theory for finding exact solutions of nonlinear evolution equations, such as the Backlund transformation method, truncated Painlevéexpansion method, the CK direct method and so on.The first chapter introduces the concept of solitons, its developments and meanings with our main work.In the second chapter, the Painlevéproperty and its new development are introduced.In the third chapter, the recursion operator and the total resonances of the modified KdV equation are obtained by the use of Painlevéanalysis.In the forth chapter, exact travelling wave solutions to several nonlinear evolution equations are obtained by truncated Painlevéexpansion method .In the fifth chapter, the CK direct method is extended to reduce a variable–coefficient Boussinesq equation and some new similarity solutions are found. A few mistakes in [57] are also corrected.