This work utilizes Lax integrability and the Hirota bilinear approach to examine cold bosons in a zig-zag optical lattice. Such a configuration is frequently employed to elucidate various intricate phenomena in fluid dynamics, quantum optics, and plasma physics. We validated the integrability of the underlying nonlinear evaluation equation by formulating a Lax pair. Subsequently, the Hirota bilinear approach is employed to simplify the derivation of soliton solutions by converting nonlinear partial differential equations into bilinear form. This method further facilitates the construction of multi-soliton solutions through disturbance expansion. Various soliton solutions are determined and visually demonstrated through two- and three-dimensional representations. The derived soliton solutions provide essential insights that enable applied mathematicians, theoretical physicists, and engineering researchers to gain a deeper understanding of the physical significance of the model. To the best of our knowledge, the Lax pair integrability and the obtained solutions for the studied equation are new and have not been reported before.
Ahmed et al. (Sat,) studied this question.