Painleve Analysis and Soliton Solutions for Nonlinear Evolution Equations

Abstract

Solitons are the special types of solitary waves which does not change their shape and speed during propagation. When a light pulse in space or time travels in some host medium, it does not dispersive or diffract is called optical solitons (OS). Basically solitons are solu tions of special kind of nonlinear partial differential equation (NLPDE)and only integrable NLPDE's gives the soliton solutions. In this thesis, we study various kinds of soliton solutions of a couple of NLPDEs. We will obtain various type of solition solutions like solitary wave solutions, soliton wave solu tions, and different type of rational solution such as periodic rational and soliton rational solutions with the aid of unified method (UM). We will also investigate the integrability of our governing model by means of Painlev´e test (P-test). Any equation which satisfy the P-test shows that our governing model is resolvable with the help of inverse scattering transformation (IST). The equations which satisfy the P-test shows that these are integrable and gives the soliton solutions. There are many techniques in literature for the soliton solu tions of completely integrable NLEEs by transforming the equations into linear equations or with the aid of IST