Painlevé Properties Of The GCKdV Equations And Exact Solutions Of Several Nonlinear Equations

An exciting and extremely active area of research investigation during the past twenty years has been the study of Solitons and the related issue of the construction of solutions to a wide class of nonlinear equations. Such investigation push people into the research of the so-called integrability of the nonlinear systems. Up to now, numerous methods are established by mathematicians and physicists to prove the integrability of nonlinear equations. Painleve analysis is one of the most effective methods.This dissertation begins with a brief description of the discovery and the meaningful development of the soliton, together with our main purpose of this article. The second chapter contains the evolution of the Painleve analysis, ARS test approach, WTC method, perturbative, and extended Painleve methods. In this case the GCKdV system is discussed in details. It is shown that the consistence conditions of all the index are satisfied, which reveals...