الفهرس | Only 14 pages are availabe for public view |
Abstract The main objective of this thesis is to investigate connections between some analytic techniques that are used for solving some nonlinear partial differential equations of math physics. On utilizing these techniques, a number of new solutions for some nonlinear evolution equations and new similarity reductions for KS and Fisher equations are obtained. The thesis is organized as follows: Chapter one presents a brief historical view of partial differential equations and focuses on a famous class of equations that evolve in time. A literature review presents an overview for some analytic techniques for solving nonlinear partial differential equations. Finally, the work objective and action plan are illustrated. Chapter two presents a number of analytical techniques for solving nonlinear evolution equations, namely, the homogenous balance method, the polynomial ansatz, the tanh, the extended tanh, the hyperbola, and the sinecosine methods. A brief summery for each technique is presented and followed by applying it to some nonlinear evolution equations. Chapter three is devoted to illustrate the direct reduction method. First, a literature review about the reduction methods is introduced followed by a brief summery and outline of the method. On utilizing the direct reduction method for KS and Fisher equations, new similarity reductions are obtained. In chapter four, the connections between the wellknown techniques are discussed. Chapter five is devoted to present conclusion remarks and future work |