Optical Solitons and Dynamical Structures for the Zig-zag Optical Lattices in Quantum Physics

This paper investigates the widely used Zig-zag optical lattice prototype for cold bosonic atoms. This prototype generally represents nonlinear waves in plasma physics and fluid mechanics. To obtain soliton solutions, two different techniques are used, the Kumar-Malik method and the improved F-expansion approach. These solutions include periodic, kink, combo dark-bright, bright, and dark types of soliton solutions. The conducted soliton solutions show that the approach is capable of identifying a wide range of wave patterns in nonlinear partial differential equation (NLPDE) models and is also compatible, effective, and scientifically efficient. Using the Maple software, 3D, contour, density and 2D structures were created for various values of the relevant parameters in order to do numerical simulations of the outcomes. To the best of our knowledge, no previous study has explored this equation to such an extent. All the solutions obtained are verified using the Maple software application, ensuring their accuracy and correctness.