On continuum model analog to zig-zag optical lattice in quantum optics

A discrete model governing a system of cold bosonic atoms in zig-zag optical lattices in quantum optics was proposed in the literature. In an analog to this model, a continuum model is, here constructed. The resulting equation is a nonlinear Schrodinger equation NLSE with drift force and linear growth. Exact solutions of this equation are obtained. To this issue, a new transformation that allows to inspect the optical lattice due to soliton–periodic wave collision is introduced. Here, the colliding dynamics are inspected. A class of polynomial and rational solutions of the model equation constructed are obtained by using the unified and generalized unified methods. The solutions found reveal the propagation of local zigzag-shaped pulses in optical lattices. Mixed smooth–sharp (shock-like) optical pulses are also observed. This leads to the issue that the collision is locally elastic (or inelastic). Furthermore, self-modulation zigzag-shaped pulses with compression, are remarked. We mention that the zigzag-shaped pulses, in an optical lattice, was not found in the literature. Thus, the results found in this work are original. It is found that the polarization of zig-zag optical lattice is self-focusing.