Discretization of coupled modified KdV equations

The coupled modified KdV equation partial derivative v(i)/partial derivative t + 3 [(j,k=1)Sigma(N)c(j,k)v(j)v(k)] partial derivative v(i)/partial derivative x + partial derivative(3)v(i)/partial derivative x(3) = 0, i = 1,2,...,N, is discretized in the form v(i.n)(m+1) - v(i.n)(m) + delta [1 + (j.k=1)Sigma(N)c(j,k)v(j,n)(m)v(k,n)(m)] Gamma(n)(m) [v(i,n+1)(m)-v(i,n-1)(m divided by 1)] = 0, i = 1,2...,N, Gamma(n-1)(m) = [1 + (j,k=1)Sigma(N) c(j,k)v(j,n)(m)v(k,n)(m)] Gamma(n)(m)/ [1 + (j,k=1)Sigma(N)c(j,k)v(j,n)(m+1)v(k,n)(m+1)], where Gamma(n)(m) is an auxiliary variable. We integrate the difference equation numerically and compare the results with exact solutions. (C) 1999 Published by Elsevier Science Ltd. All rights reserved.