Approximate Jacobi elliptic function solutions of the modified KdV equation via the decomposition method

The scheme is developed to obtain approximate Jacobi elliptic function solutions of the modified KdV equation with initial conditions via the Adomian decomposition method. As consequence, we derive the approximate solution and exact Jacobi elliptic function solutions of the modified KdV equation with initial conditions. The approximate solution is compared with the exact solution. Moreover we analyze the absolute error and relative error, and give the contour and density plots of the approximate Jacobi elliptic function solutions with different modulus m = 0.25, 0.5, 1.