Analytical approximate solution for the forced korteweg-de vries (fkdV) on critical flow over a hole using homotopy analysis method

Free surface flows in a two-dimensional channel past over a hole is studied using shallow water forced korteweg-de vries (fkdv) equation. the forcing term of fkdv equation represents the hole shaped bottom topography. froude number (fr),which represents the ratio of flow speed to the wave speed,will also be used in solving fkdv equation. the fkdv equation is solved using homotopy analysis method (ham). ham is an approximate analytical technique used to obtain series of solutions for the nonlinear problems where ham has an auxiliary parameter coto adjust and control the convergence region of the series solution. solitary wave solutions are obtained from the series of solutions of ham and wave flows are observed at particular time. the ham solution shows the hole shaped bottom topography plays an important role in determining the evolution of solitary waves. © 2016 penerbit utm press. all rights reserved.