الفهرس 
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Abstract
Many different phenomena in physics can be described as nonlinear phenomena. All of these nonlinear phenomena can be modeled mathematically with nonlinear differential equations. In this work some nonlinear phenomena in physics are studied. 1. The coagulation phenomena that is a very important process in a wide variety of physical, chemical and biological processes. Consequently, an understanding of its kinetics is of great interest in many problems ranging as colloidal polymer technology, coagulation DROPs in clouds, growing gas bubbles in solids and liquids, fuel mixtures in engines, star formation, and antigenantibody aggregation and cluster formation in galaxies. Smoluchowski?s equation for rapid coagulation describes the temporal evolution of a system of particles, which are continuously growing as result of pairs of particles coming into contact and bonding to form clusters. Examples of this process include the coagulation of aerosols. The coagulation with mass loss of aerosols is studied for different forms of kernel and initial conditions, where the data show the effect of the mass loss on the concentration function. 2. The phenomenon of fluid flows in thick cylinder tube is studied, where the viscosity of the fluid is ignored, the propagation of weakly nonlinear waves in the longwave approximation is investigated. Depending on the balance between nonlinearity and dissipation or dispersion. The evolution equations are obtained as follow. Kortwegde Vries equation, which results by balancing the nonlinearity with dispersion. Modified Burger?s equation, which results by balancing the nonlinearity with dissipation. And modified Kortwegde Vries equation, which results by balancing the nonlinearity with dispersion. 3. The nonlinear Boltzmann problem or the transport theory become an extremely important topic in physics, and engineering, since particle transport processes arise in a wide variety of physical phenomena. Much of the early development of this theory was stimulated by astrophysical studies of radiant energy transfer in stellar or planetary atmosphere. Transport theory was applied in many fields such as nuclear medicine, in reactor physics, the motion of high energy charged particles such as electrons or light ions, and the transport in ionized gases and plasma. The nonlinear Boltzmann problem is studied in two different cases. The problem is converted into the moment equation and introducing the generating function for the moments, a nonlinear differential equation is obtained. There are many different methods for solving the nonlinear partial differential equation among these methods, two different methods used for solving these problems that are: 1. Adomian decomposition method (ADM). 2. Variational iteration method (VIM). The ADM and the VIM are two of the simplest mathematical methods to give approximate solutions for the nonlinear differential equations, but it is hard to have closed form solution by these methods. The VIM is easier than ADM where it leads to the same solution.