An application of the modified Adomian decomposition method for (NÂ +Â 1)-dimensional sine-Gordon field

Based upon the modified Adomian decomposition method, a scheme is developed to obtain approximate Jacobi elliptic function solutions of the (N + 1)-dimensional sine-Gordon field with initial conditions. As a result, we derive the approximate solution and exact Jacobi elliptic function solution of the (N + 1)-dimensional sine-Gordon field with initial conditions. Moreover the approximate solution is compared with the exact solution with N = 2 and with different modulus K = 0.25, 0.5 and 1.