A Study On The B Family Of Shallow Water Wave Equations

In this dissertation we study b family of shallow water wave equations which include classical Korteweg-de Vries, Camassa-Holm and Degasperis-Procesi equations. We first establish the models of the Camassa-Holm and Degasperis-Procesi equations, deriving them from the shallow waterwave argument and then compare a large class of properties relating to the two equations. Then we consider the b family equation as the parent equation and derive the above mentioned two equations as special cases of the b-family as well as the classical KdV equation.Next we establish results of local well-posedness using Kato's semigroup theory,global existence and blow up solutions under certain special initial profiles(periodic) and relate those to periodic b-family equation.Keywords:Camassa-Holm(CH) and Degasperis-Procesi(DP)equations; periodic b-family ;blow-up;local existence;global existence.