  In this work, an exact solution to a new generalized nonlinear KdV partial
differential equations has been investigated using homotopy analysis
techniques. The mentioned partial differential equation has been solved using
homotopy perturbation method (HPM). In details, the study is divided into two
cases; the first case is that the linear part is the velocity (the first
derivative with respect to time), and the initial guess was chosen at the
initial time or the boundary values. Next, the other case was that the linear
part consists of many linear terms from the equation, the chosen terms
constructed a partial differential equation whose solution can be gained
easily. Eventually, some plots of the found solutions have demonstrated the
convergent behaviors of the solutions.
