Khare, A.,Cooper, F.,Saxena, A.

We consider the coupled nonlinear Dirac equations (NLDEs) in 1 + 1 dimensions with scalar-scalar self-interactions g(1)(2)/2((psi) over bar psi)(2) + g(2)(2)/2((phi) over bar phi)(2) + g(3)(2)((psi) over bar psi)((phi) over bar phi) as well as vector-vector interactions of the form g(1)(2)/2((psi) over bar gamma(mu)psi)((psi) over bar gamma(mu)psi) + g(2)(2)/2((phi) over bar gamma(mu)phi)((phi) over bar gamma(mu)phi) + g(3)(2)((psi) over bar gamma(mu)psi)((phi) over bar gamma(mu)phi). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form psi = e(1)(-i omega)(t){R-1 cos theta, R-1 sin theta}, phi = e(2)(-i omega)(t){R-2 cos eta, R-2 sin eta}, and assuming that theta(x), eta(x) have the same functional form they had when g(3) = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for R-i(x) which are valid for small values of g(3)(2)/g(2)(2) and g(3)(2)/g(1)(2). In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrodinger equation for which we obtain two exact pulse solutions vanishing at x -> +/-infinity.