ON SOLUTION METHODS FOR SOME NONLINEAR DIFFERENTIAL EQUATIONS

Abstract

The aim of this thesis is to investigate some selected nonlinear partial differential equations in mathematical physical. New analytical exact solutions are obtained including real solutions, complex solutions, soliton solutions, periodic solutions, single soliton solution, kink soliton solutions, singular soliton solutions, hyperbolic function solutions, trigonometric function solutions, bright soliton solutions, Jacobi elliptic function solutions, rational function solutions, Bell-type solitary wave solutions, and other solutions by stratifying several methods. These methods are the extended simplest equation method, the extended auxiliary equation method, the fractional Riccati method, the rational fractional -expansion method, the modified simple equation method, the -expansion method, the two variables -expansion method, the -expansion method, the new Sub-ODE method and the simplified Hirota’s method. The importance of researching this topic is to investigate the validity of extending and applying some analytical methods for solving some famous partial differential equations in a trial to present new exact analytical solutions which is considered important for mathematicians, physists, and engineers. The objective of this thesis is to be considered as a guidline for researches in this field to further improve such methods to suit more nonlinear partial diffrential equations. We conclude here that our researh work presents new analytical solutions using some powerful methods. These new solutions are in complete agreement and comparable well with other existing results in literature. The thesis contains six chapters in addition to english and arabic summaries classified follows: Chapter I: This chapter deals with the introduction and a brief description of the considered methods. Bird’s eye view of the mathematical methods used to obtain the exact solutions for the selected nonlinear partial differential equations are given in chapters II up to VI.