Mansour Shiralizadeh - Department of Mathematics, Payame Noor University (PNU), Tehran, Iran.
Amjad AliPanah - Department of Applied Mathematics, University of Kurdistan, Sanandaj, Iran.
Maryam Mohammadi - Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran.

In this paper, we use the rational radial basis functions ( RRBFs) method to solve the Korteweg-de Vries (KdV) equation, particularly when the equation has a solution with steep front or sharp gradients. We approximate the spatial derivatives by RRBFs method then we apply an explicit fourth-order Runge-Kutta method to advance the resulting semi-discrete system in time. Numerical examples show that the presented scheme preserves the conservation laws and the results obtained from this method are in good agreement with analytical solutions.

KdV equation, RBF, rational radial basis function method, Runge-Kutta method