Approximate interacting solitary wave solutions for a pair of coupled nonlinear Schrödinger equations

Using a modified Cole-Hopf transformation and the Hirota method for series solutions, approximate interacting solitary wave solutions for a pair of coupled nonlinear Schr\"odinger equations have been investigated. Previous solutions have been regained. It is noted that if the solution of the first order term satisfied by the Schr\"odinger equation for a free particle has been taken as a linear superposition of the solutions, then the envelope of the interacting solitary waves are time dependent. If the coupling coefficient is negative, then the amplitudes of the envelope interacting solitary waves are reduced from those in the decoupled limit.