These equations are given by where ψ$_{k}$ = ψ$_{k}$ ( x, t ) , the functions, v$_{k}$ ( x, t ) , are the trapping potentials, and the g$_{ij}$, ( i, j = 1 , 2) describe the strength of the cubic nonlinearities. Note that we are using standard notation, with both the fields and coordinates dimensionless. Note also tha t we are supposing that our model describe 1D BEC, and then it should engender cigar-shaped traps to induce tight confinement in two transverse directions, leaving the condensate almost free along the x axis. In the super- chemistry model of [7, 8], the above equations are amended by a term which goes as √$_{2}$$_{αψ}$$_{1}$$_{ψ}$$_{2}$ in Eq. (1) and with a term of α √$_{2}$ ψ 2 1 in Eq. (2). These, number-nonconserving, terms arise from treating the Feshbach resonance as a coupling term between atoms and molecules. It is interesting to comment here that the elimination of, say, ψ$_{2}$ in favor of an effective equation for ψ$_{1}$ , would necessarily end up with a GP equation with depletion effect. This could appear in the form of complex nonlinearity. We leave such study for a future work. In the following we seek to reduce the above two equations into the following pair of equations with µ$_{i}$ and the G$_{ij}$ being constants. We achieve this with the use of the two Anzatse : However, we now have to have 3 ∂ ∂x ( ρ $_{2}$∂ζ ∂x ) = 0 . (9) ∂ζ ∂t + 2 ∂η ∂x ∂ζ ∂x = 0 , (8) ρ ∂ρ ∂t + ∂ ∂x ( ρ $_{2}$∂η ∂x ) = 0 , (7) ψ$_{2}$ ( x, t ) = ρ ( x, t ) e iη ( x,t $^{)}$A$_{2}$ ( ζ ( x, t )) . (6) ψ$_{1}$ ( x, t ) = ρ ( x, t ) e iη ( x,t $^{)}$A$_{1}$ ( ζ ( x, t )) , (5) µ$_{2}$A$_{2}$ = − ∂ $^{2}$A$_{2}$ ∂ζ 2 + 2 ∑ k =1 ( G$_{2}$$_{k}$ | A$_{k}$ | $^{2}$) A$_{2}$, (4) µ$_{1}$A$_{1}$ = − ∂ $^{2}$A$_{1}$ ∂ζ 2 + 2 ∑ k =1 ( G$_{1}$$_{k}$ | A$_{k}$ | $^{2}$) A$_{1}$, (3) i ∂ψ$_{1}$ ∂t = − ∂ $^{2}$ψ$_{1}$ ∂x 2 + v$_{1}$ ( x, t ) ψ$_{1}$ + 2 ∑ k =1 ( g$_{1}$$_{k}$ ( x, t ) | ψ$_{k}$ | $^{2}$) ψ$_{1}$, (1) i ∂ψ$_{2}$ ∂t = − ∂ $^{2}$ψ$_{2}$ ∂x 2 + v$_{2}$ ( x, t ) ψ$_{2}$ + 2 ∑ k =1 ( g$_{2}$$_{k}$ ( x, t ) | ψ$_{k}$ | $^{2}$) ψ$_{2}$, (2)