A Chebyshev spectral method for solving Korteweg–de Vries equation with hydrodynamical application

It is well known that many hydrodynamical problems appearing in the study of shallow water theory or the theory of rotating fluids, can be reduced to Korteweg–de Vries equation subject to certain initial and boundary conditions. In this work, a Chebyshev spectral method for obtaining a semi-analytical solution to such equation is presented. One numerical application is considered to show how we can apply the presented proposed method. A comparison between our results and the numerical results obtained by the Hopscotch method are made.