The Extended Sech Function Method and The Cole-Hopf Transformation for Solving the Nonlinear Korteweg-de Vries Equation

M. M. El-Horbaty, F. M. Ahmed

Abstract: In this paper, we are using the extended sech function method along with a type of cole-Hopf transformation to obtain the solutions for the nonlinear Korteweg de Vries (KdV) equation. These types of solutions are represented as the hyperbolic function solutions including the solitary wave solution, shock wave solution and trigonometric function solution when the modulus approaches to 1 and 0. Mathematica software is used in calculation and graphics.

Keywords: Cole-Hopf transformation, Extended Sech function, Korteweg de Vries KdV equation, Solitary travelling wave solutions