Constructing The Exact Traveling Wave Solutions For Nonlinear Partial Differential Equations

The nonlinear partial differential equations(NLPDEs)have numerous applications in the field of applied mathematics,physics,engineering,biology,chemistry,control science,oceanic sciences,fluid dynamics,biophysics,nonlinear optics and field theory.However,obtaining solutions of the NLPDEs is one of the most difficult tasks in mathematics,physics and engineering.This thesis has considered the problem of applying and modifying existing methods to obtain the analytical solutions for a specific class of NLPDEs.We presented the algorithm of each method and further explains a conceptual framework linking the facets in finding the traveling wave solution for NLPDEs.The Riccati equation rational expansion(RERE)method is implemented to construct a series of solutions including rational solitary wave solutions,rational wave solutions and periodic wave solutions for the generalized(2+1)-dimensional Boussinesq equation and the nonlinear couple Drinfel'd-Sokolov-Wilson(DSW)system.Some of the obtained solutions are demonstrated graphically by assigning a constant value to each of the parameters.The extended ((G?(?))/(G?(?)))-expansion method is also implemented to study the analytical wave solutions for the nonlinear three-dimensional modified Korteweg-de Vries-Zakharov-Kuznetso and the two-dimensional nonlinear Kadomtsev-Petviashvili-Burgers equations.Using the extended modified direct algebraic method,the soliton and additional solutions of the 3D mKdV-ZK and the coupled(2+1)-dimensional nonlinear KD equations are found.The attained new solutions include bright soliton,singular periodic,dark singular combo optical soliton,plane wave solution,Jacobi elliptic function and Weierstrass elliptic function solutions.Some of the obtained solutions are demonstrated graphically to show the evolution shapes of the solutions.Finally,the improved F-expansion method is also implemented to attain the wave solutions of the nonlinear fractional Zakhorov-Kuznetsov-Benjamin-Bona-Mahony and fractional symmetric regularized long wave equations.The new solutions attained are in the form of hyperbolic and trigonometry solutions.This thesis has established various new solutions for specific class of NLPDEs,demonstrating the effectiveness and superiority of the suggested methods.