The quasi-wavelet solutions of MKdV equations

The quasi-wavelet method is used for obtaining the numerical solution of the MKdV equation. The quasi-wavelet discrete scheme is adopted to make the spatial derivatives discrete, while the fourth-order Runge-Kutta method is adopted to make the temporal derivative discrete. One of the MKdV equation u(t) + 6 u(2)u(x) + u(xxx) = 0, which has an analytical solution, is solved numerically. The numerical results are well consistent with the analytical solutions, even at t = 10000s.