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.