Technical report: solutions of Korteweg-de Vries (KdV) equation / Faizatul Asyekin Yusri, Rusya Iryanti Yahaya and Nurhidayah Mat Ramli

In the present work, the derivation of Korteweg-de Vries (KdV) equation and its single­ soliton solution are shown step by step to give better understanding to people. This project is only devoted to shallow water waves where the derivation of KdV equation by using Euler equation in ( 1 + 1) dimensions is proposed. In the derivation, a set of governing equations is used and it follows the assumption of irrotational two-dimensional motion of an incompressible inviscid fluid that is bounded above by a free surface and below by a rigid horizontal plane. Then, scaling and substitution method are implemented. In addition, the far-field variables for wave that propagate to the right are also utilised. After solving the KdV equation, single-soliton solution for standard KdV equation is obtained from traveling wave solution which is one of the D' Alembert equation method. This project is then completed by sketching and plotting the graphs of solitons using Maple. These graphs illustrated the propagation of single-soliton solution to the right, left and both side of the graph.