الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The reductive perturbation theory has been employed to derive some nonlinear differential equations, which describe problems in plasma physics such as the Korteweg-de Vries (KdV) and Kadomstev-Petviashvili (KP) equations for small but finite amplitude electrostatic waves. A new algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV and KP equations, has been used. Numerical studies for some plasma environments have been made using plasma parameters reveal different solutions such as bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called blowup solutions in addition to the propagation of an explosive pulses. Generalized variable-coefficient combined KdV-mKdV equations arising in nonlinear lattice, plasma physics and ocean dynamics are investigated. Several new families of exact solutions of physical interest are obtained. These solutions involved abundant temporally-inhomogeneous features. A method for solving the nonlinear evolution equations with self-similar solutions is presented. The method employs ideas from symmetry reduction to space and time variables and similarity reductions for nonlinear evolution equations are performed. The solutions were obtained with a coefficient parameters depend on the studied model and can be in the form of new types of solitary, shock and periodic waves. Also, the method can be applied to other nonlinear evolution equations in mathematical physics. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments (viz. the cusp of the terrestrial magnetosphere, the geomagnetic tail, the auroral regions, the ionosphere, etc.).