### Abstract:

Nonlinear evolution have equations a major role in various scientific and engineering fields , such as fluid mechanics , plasma physical , optical fibbers , solid state physics , chemical physics and geochemistry. Nonlinear wave phenomena of dispersion , disspation, diffusion , recation and convection are very important in nonlinear wave equation . the Schrödinger – Hirota equation which governs the propagation of optical soliton in dispersive optical fiber . Gardener equation known as the mixed Kdv – Mkdv equation is widely studied in various areas of physics that includes plasma physics Fluid Dynamics ,Quantum Field Theory, Solid State Physics and others . Perturbed Burgers equation appears in the study of gas dynamics and also in free surface motion of waves in heated fluids . the Davey-Stewartson [i - ii] equations are tow two will known examples of integrable equation in two special dimensions, which arise as higher dimensional generalizations of the nonlinear Schrodinger equation. The generalized Sakharov equation plays an important role in nonlinear physical science , which is describe various natural phenomena such as vibrations , and others . In this thesis we aim to find new exact solution of the k (n+1 , n+1) equation Schrödinger – Hirota equation , Gardner equation , modified Kdv equation , Perturbed Burgers equation , General Burgers - Fisher equation , and Cubic modified Boussinesq equation . most of other technics for solving nonlinear partial differential equations have their in built deficiencies including evaluation of so -called A domains polynomials , divergent result , successive applications of the integral operator un-realistic assumptions , non- compatibility with nonlinear of physical problem and very lengthy calculations . the method have established scientific value and reliability. we applied a reliability new technique which is called sine cosine method, and the modified extended tanh method , these methods are efficient for obtaining exact soliton solution of nonlinear partial differential equations we recommend to apply this methods for solving system of other nonlinear partial differential equations .

### Description:

A Dissertation Submitted to the University of Gezira in Partial Fulfillment of the Requirements for the Award of the Degree of Master of Science in Mathematics Department of Mathematics Faculty of Mathematical and Computer Sciences,May, 2016