Generalized Korteweg-de vries (KdV) type equations

In this thesis, a third order integrable non-linear general equation is given, which includes five different equations such as non-linear partial differential KdV, Schamel, Schamel- KdV, Modified-Benjamin-Bona-Mahony and Benjamin-Bona-Mahony equation. By using a simple transformation, this given third order non-linear partial differential equation was transformed into a non-linear third order ordinary differential equation. It was reduced to an equation that can be integrated twice and separated into first order variables. An elliptic integral was achieved in the integration of the equation that can be separated into these variables obtained in the general case, but in the general case the solution could not be obtained from the known elementary functions. In some special cases the exact solutions of Schamel-KdV, Schamel, KdV, Modified-Benjamin-Bona- Mahony and Benjamin-Bona-Mahony equations were reached with the help of elliptic type integrals. Detailed and comparative graphs of some of the obtained solutions for different parameters were drawn in two and three dimensions.