الملخص الإنجليزي
In chapter 1, starting with linear and nonlinear waves, we introduce the concept
of solitary wave solutions (SWS) which arises due to a balance in weak nonlinearity
and dispersion and compacton solutions which are a result of strong nonlinearity and
dispersion. In chapter 2, SWSs of Korteweg de Vries (KJV) equation, a modified
KdV (mKdV) equation and Boussinesq equation have been derived. These equa
tions are models for nonlinear long waves in shallow water and several other physical
situations. The generalized KDV equation known as Kadomtsev-Petviashvili (KP)
equation in two space variables has also been solved using the Adomian Decompo
sition method to derive SWSs. In chapter 3, Tanh-coth method has been used to
derive SWSs of KDV equation , mKdV equation, a generalized KdV equation in one
variable, a generalized KdV equation with two power nonlinearities, the potential
equation and the Gardner equation. In chapter 4, compacton solutions have been
derived for K(n,n) equation and K(n+1,n+1) equations. Maple has been used to
draw graphs of many solutions.
