Nonlinear Schrodinger equation (NLSE) is the fundamental equation which describes the wave field
envelope dynamics in a nonlinear and dispersive medium. However, if the fields have many
components, one should consider the Coupled Nonlinear Schrodinger equation (CNLSE). We
considered the interactions of orthogonally polarized and equal-amplitude vector solitons with two
polarization directions. In this paper, we focused on the effect of Gaussian potential on the scattering
of the vector soliton in CNLSE. The scattering process was investigated by the variational
approximation method and direct numerical solution of CNLSE. Analytically, we analyzed the dynamics
of the width and center of mass position of a soliton by the variational approximation method. Soliton
may be reflected from each other or transmitted through or trapped. Initially, uncoupled solitons may
form the coupled state if the kinetic energy of solitons less than the potential of attractive interaction
between solitons but when its’ velocity above the critical velocity, the soliton will pass through each
other easily. Meanwhile, a direct numerical simulation of CNLSE had been run to check the accuracy
of the approximation. The result of the variational model gives a slightly similar pattern with direct
numerical simulation of CNLSE by fixing the parameters for both solutions with the same value. The
interaction of the vector soliton with Gaussian potential depends on the initial velocity and amplitude
of the soliton and the strength of the external potential