Technical report: the mathematical modelling of shallow water wave: Korteweg de Vries Equation (KdV) / Nor Aniza Mohd Nasir, Nik Nur Izny Aqila Sapri and Nik Nurfatinliyana Kamarudin

In this report, the study have been conducted on a nonlinear waves equation, Korteweg­de Vries (KdV), arising in mathematical modelling and the investigating existence of solutions to these equation using variational methods. In particular, the traveling wave solution is known as solitary waves. The focus is on the derivation of the Korteweg-de Vries equation and the solution for these equations. For methodology, there are two methods that have been used which are exact equation to the Kdv Equation using D' Alembert Method and Exact Solution with Backlund transformation (Bilinearization). Exact equation to the KdV equation using D' Alembert method are leads to two waves represents by f (x-ct) which is a wave that move towards right with speed c and f (x +ct) which is wave that move towards left with speed c. Next, the method is Backlund transformation. By using this method it provides the approach to the theory of solitary wave. The arbitrary function is used to obtain the dependent variable transformation. After that the next step is to get the two soliton solutions by using the mathematical code. The method of Backlund transformation create a non-linear equation presenting the soliton solution. The KdV equation is rewritten in a bilinear form in order to find the Backlund transformation for equation KdV. To obtain the result, maple code are being used. Maple are being used to plot the graph of one soliton and two soliton solution waves. It has been plotted in 2d graph. For the conclusion, there is comparison between D' Alembert method and Backlund Transfor­mation method to determine which method is more easier.