Numerical solutions of KdV equation using radial basis functions

Numerical solution of the Korteweg-de Vries equation is obtained by using the meshless method based on the collocation with radial basis functions. Five standard radial basis functions are used in the method of the collocation. The results are compared for the numerical experiments of the propagation of solitons, interaction of two solitary waves and breakdown of initial conditions into a train of solitons.