Painlevé Test For Some Nonlinear Evolution Equations

The integrability of nonlinear system is a very important topic. Completely integrable system is a special and important part of nonlinear system. Com-pletely integrable systems and Painleve properties are closely linked. The WTC method is one of the most effective methods to the nonlinear evolution equa-tions for Painleve test. The Kruskal simplified method can greatly simplify the Painleve test.The content of this paper mainly divided into the following four parts:The first chapter, we mainly introduce the background and significance of the research object.The second chapter, the basic theoretical knowledge of the thesis is intro-duced in detail.The third chapter, we apply the WTC method combined with Kruskal al-gorithm to carry Painleve tests of the following equations.The highly dispersion DGH equationThe varying coefficient KdV equationsThe fourth chapter, we apply the WTC method combined with Kruskal algorithm to carry Painleve tests of the following equations.The coupled mKdV equationsClassieal Boussinesq equations...