In this paper, we consider the propagation of a spatial soliton in a waveguide with triangular linear refractive index profile. We propose a model that is obtained by starting with a small perturbation of the constant linear refractive index in the displacement vector of the Maxwell equation, and then deriving the NLS equation for this case. Using this model it is shown, both analytically and numerically, that the soliton beam oscillates inside the waveguide. This is as expected, but differs from the model found in the literature in which the inhomogeneity is introduced directly in the standard NLS equation. Finally, the proposed model is used to study the breakup of bound N-soliton in a triangular waveguide.