【作者】 于海杰；

【导师】 斯仁道尔吉；

【作者基本信息】 内蒙古师范大学 ， 应用数学， 2008， 硕士

【摘要】 本文研究内容主要涉及孤立子理论中精确求解非线性发展方程的Backlund变换法,Painlevé截断展开法,CK直接约化法等几个方面。引言中主要介绍了孤立子概念的产生、孤立波的发展及其意义和本文的主要工作。第二章介绍了Painlevé分析法及其新进展。第三章利用Painlevé分析法得到了修正KdV方程的递推算子及其共振点。第四章应用Painlevé截断展开法求解了几个非线性发展方程。第五章在修改文献[57]几处笔误的基础上应用CK直接约化法求解了一类描述方向上存在可变剪切流动的长波变系数Boussinesq方程的相似解,这种解不同于用Painlevé截断展开法求出的解。更多还原

【Abstract】 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.更多还原